Show that: [tex]\sqrt[ab]{ \frac{ {x}^{a} }{ {x}^{b} } } . \sqrt[bc]{ \frac{ {x}^{b} }{ {x}^{c} } } . \sqrt[ca]{ \frac{ {x}^{c} }{ {x}^{a} } } = 1.[/tex]

Brainliest! Brainliest..ans.

Answers

Answer 1

Here we need to Prove that ,

[tex]\bf\implies \sqrt[ab]{ \frac{ {x}^{a} }{ {x}^{b} } } . \sqrt[bc]{ \frac{ {x}^{b} }{ {x}^{c} } } . \sqrt[ca]{ \frac{ {x}^{c} }{ {x}^{a} } } = 1.[/tex]

Lets start with LHS , which is ,

[tex]\bf\implies LHS = \sqrt[ab]{ \dfrac{ {x}^{a} }{ {x}^{b} } } . \sqrt[bc]{ \dfrac{ {x}^{b} }{ {x}^{c} } } . \sqrt[ca]{ \dfrac{ {x}^{c} }{ {x}^{a} } } [/tex]

We know that ,

[tex]\bf\implies \sqrt[n]{k^m }= k^{\frac{m}{n}}[/tex]

• So that ,

[tex]\bf\implies \sqrt[ab]{x^{a-b}} . \sqrt[bc]{x^{b-c}} .\sqrt[ac]{x^{c-a}} \\\\\bf\implies x^{\frac{a-b}{ab}} . x ^{\frac{b-c}{bc}} .x^{\frac{c-a}{ca}} \\\\\bf\implies x^{\frac{ ac - bc + ab - ac + bc - ba }{abc } }\\\\\bf\implies x^{\frac{0}{abc}} \\\\\bf\implies x^0 \\\\\bf\implies 1 = RHS [/tex]

Hence ,

[tex]\implies \boxed{\bf \red{ LHS = RHS }} [/tex]

Answer 2

[tex]\large\underline{\sf{Solution-}}[/tex]

Consider LHS:

[tex]\sf= \sqrt[\sf ab]{\dfrac{\sf x^{a}}{\sf x^{b}}}\cdot \sqrt[\sf bc]{\dfrac{\sf x^{b}}{\sf x^{c}}}\cdot \sqrt[\sf ac]{\dfrac{\sf x^{c}}{\sf x^{a}}}[/tex]

As we know that:

[tex]\sf\red\leadsto\dfrac{x^{a}}{x^{b}}=x^{a-b}[/tex]

We get:

[tex]\sf= \sqrt[\sf ab]{\sf x^{a-b}}\cdot \sqrt[\sf bc]{\sf x^{b-c}}\cdot \sqrt[\sf ac]{\sf x^{c-a}}[/tex]

We can also write it as:

[tex]\sf= x^{\dfrac{a-b}{ab}}\cdot x^{\dfrac{b-c}{bc}}\cdot x^{\dfrac{c-a}{ac}}[/tex]

We know that:

[tex]\sf \red\leadsto x^{a}\cdot x^{b}=x^{a+b}[/tex]

We get:

[tex]\sf= x^{\bigg(\dfrac{a-b}{ab}+\dfrac{b-c}{bc}+\dfrac{c-a}{ac}\bigg)}[/tex]

[tex]\sf= x^{\bigg(\dfrac{c(a-b)+a(b-c)+b(c-a)}{abc}\bigg)}[/tex]

[tex]\sf= x^{\bigg(\dfrac{ac-bc+ab-ac+bc-ab}{abc}\bigg)}[/tex]

[tex]\sf= x^{\bigg(\dfrac{0}{abc}\bigg)}[/tex]

[tex]\sf= x^{0}[/tex]

[tex]\sf=1[/tex]

[tex]\textsf{= RHS}\\[/tex]


Related Questions

If there are 2,000 females and 2,000 males enrolled at a college and four different students are randomly selected to receive a book scholarship, what is the probability that at least one is female?

Calculate the probability two ways: a) treat as dependent selections and b) treat as independent selections.

Answers

Answer:

500

Step-by-step explanation:

you just divide 2000 by 4 and get 500

103.468 round this to the nearest liter

Answers

Answer:

103

Step-by-step explanation:

So the .4 in the tenths place is less than 5 it is rounded down/stays the same so its 103

Hope this helps!!

Have a nice day! :D

please help me with this sum​

Answers

Answers:

59 × 9 = 531

63 × 8 = 504

83 × 4 = 332

38 × 5 = 190

72 × 6 = 432

48 × 4 = 192

19 × 3 = 57

58 × 2 = 116

73 × 8 = 584

60 × 7 = 420

36 × 5 = 180

56 × 7 = 392

75 × 3 = 225

63 × 6 = 378

73 × 3 = 219

70 × 5 = 350

57 × 6 = 342

53 × 7 = 371

27 × 6 = 162

29 × 4 = 116

73 × 3 = 219

49 × 9 = 441

92 × 2 = 184

57 × 9 = 513

36 × 3 = 108

Please help and answer both of the questionssss

Answers

Answer:

(n + 6) / -4 = 10

n + 6 = 10 × -4

n + 6 = -40

n = -40 - 6

n = -46

(n - 2) / -3 = -6

n - 2 = -6 × -3

n - 2 = 18

n = 18 + 2

n = 20

Step-by-step explanation:

brainliest plz

Adjoa’s gross salary for last month was Ghc4,687.24. If Ghc421.78 was deducted from Adjoa’s salary pay, how much take-home pay did Adjoa earn this past month?

Answers

Adjoa take-home pay earned for the past month is Ghc4,265.46

From the question,

We are to determine the amount of take-home pay Adjoa earn the past month

From the given information, we have that

Adjoa’s gross salary for last month was Ghc4,687.24

Also

Ghc421.78 was deducted from Adjoa’s salary pay

To determine how much take-home pay Adjoa earn the past month,

We will subtract the amount deducted from Adjoa’s salary pay from Adjoa’s gross salary for last month

That is,

Adjoa take-home pay = Ghc4,687.24 - Ghc421.78

Adjoa take-home pay = Ghc4,265.46

Hence, Adjoa take-home pay earned for the past month is Ghc4,265.46

Learn more here: https://brainly.com/question/17336888

In a project there are 560hrs

Answers

Answer:

560hrs

Step-by-step explanation:

1day=24hrs

560hrs=(560÷24)days

=23.333days

HELP!?!?!?! I can't figure this out

Answers

Answer:

So, I believe n/2 may be even and 3n+1 is odd. They succumb to 3n if that helps.

Step-by-step explanation:

I'm not certain on what to do but I hope this helps some what.

In a school 2/3 parts of the total numbers of students. 3/10 parts are between 8 to 12 years and the remaining are above 12 years . What parts of the students are above the age of 12 years.​
ans:3/10​

Answers

3/10

As you know the answer already I don't think you need any further explanation :)

given cosec theta = 7/2 find sin theta​

Answers

Answer:

Sin0=7/25

Step-by-step explanation:

See attachment. Please give step by step solution. Thank you

Answers

Answer:

x=19

Step-by-step explanation:

cross multiply

(−3)(+5)(3+5)=(−3)(+5)⋅2−3

(−3)⋅3=(+5)⋅2

3(−3)=(+5)⋅2

=19

SOMEONE HELP ME PLEASE

Answers

Your answer is 34.
5 squared plus 3 squared equals 34

Answer:

h=4

Step-by-step explanation:

the height can't be smaller than 3 and higher than 5, you're making a hypothesis.

1. find the measure of each angle

Answers

Answer:

The equation is 3x -5 + 10x -7 = 180°

Step-by-step explanation:

These angle are a linear pair. Linear pair are two angles that are adjacent and their sides are opposite rays, or the two angles form a straight angle = 180°

The equation is 3x -5 + 10x -7 = 180°

Given that the points (12, –4) and (–36, 8) lie on a line, what is the equation of the line?

Answers

The equation of the line passing through the points (12, –4) and (–36, 8) is y = -1/2 x  - 1

The formula for calculating the equation of a line is expressed as:

y = mx + b

m is the slope of the line

b is the y-intercept

Given the coordinate points expressed as (12, –4) and (–36, 8)

Get the slope:

m = 8+4/-36-12

m = 12/-48

m = -1/4

Get the y-intercept "b"

Recall that y = mx + b

8 = -1/4(-36) + b

8 = 9 + b

b = 8 - 9

b = -1

Get the required equation.

Recall that y = mx + b

y = -1/2 x + (-1)

y = -1/2 x - 1

Hence the equation of the line passing through the points (12, –4) and (–36, 8) is y = -1/2 x  - 1

Learn more here: https://brainly.com/question/17003809

Estimate the product 2.1 x 0.9

Answers

Answer:

2.0 estimated product

1.89 Actual product

Step-by-step explanation:

2.0*1.0=2.0

2.1*1.0=1.89

The product of 2.1 x 0.9 = 1.89

What is Product?

A product is something that has been multiplied one or more times. For instance, the mathematical formula "times equals" would be written with the terms "times," "multiplicand," and "product," respectively.

Given:

2.1 x 0.9

Now, Multiplying

                          2  .  1

                       x 0  .  9

                      _________

                           1  8  9

                           0  0  x

                      __________

                          1  .  8  9

Hence, the product of 2.1 x 0.9 = 1.89

Learn more about product here:

https://brainly.com/question/624355

#SPJ2

How would I find the derivative of 2^3^x^2 ​

Answers

Answer:

d

y

d

x

=

4

3

x

3

 

Explanation:

y

=

2

3

x

2

=

2

3

x

2

Applying the power rule:

d

y

d

x

=

2

3

(

2

)

x

3

=

4

3

x

3

Step-by-step explanation:

The high temperature was recorded as 23 7°F The low temperature that same day was recorded as
6.9°F
What was the difference between the high and low temperatures for that day?
Enter your answer as a decimal in the box

Answers

Answer:

The high temperature was recorded as 23 7°F The low temperature that same day was recorded as

-6.9°F

What was the difference between the high and low temperatures for that day?

Enter your answer as a decimal in the box

Answer is 30.6

Step-by-step explanation:

23.7

- 6.9

______

30.6

Have a blessed day

The difference between the high and low temperatures for that day is 30.6

what is Unitary Method?

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

The high temperature was recorded as 23 7°F = +23.7

the low temperature that same day was recorded as 6.9°F = -6.9 F

so,  difference between the high and low temperatures for that day

= 23.7- (-6.9)

= 30.6

Learn more about unitary method here:

https://brainly.com/question/22056199

#SPJ2

Yen paid $10.50 for 2.5 pounds of pretzels. What price did she pay for each pound of pretzels?

After dividing 25 into 105, the next step is to
25 by 4.
The next step is to
100 from 105.
The next step is to
the next number.

Answers

The first step is to Multiply  The next step is to Divide.

Ok so if you were wondering what to do on the box that says this

Move Decimal

Divide

Multiply

Subtract

Bring down

On this, I agree with myself. The solution is straightforward. Simply click them in the sequence listed, beginning with the first and ending with the last. Wow, what sleuthing I did. I realize it's not much, but I was perplexed by this as well, so you could be as well. So here we go with the actual answer. To tackle these sorts of issues, you must employ a technique known as PEMDAS, which stands for.

Parenthisis

Exponent

Multiply

Divide

Add Subtract

I realize I spelt the first one incorrectly, but it's 2 a.m. and I'm doing homework for you. Now we must consider whether or not this has any parenthesis. This particular issue does not. Now we must determine whether or not this issue has exponents, which it does. As mentioned in the response box on the lesson's main page. So we have to consider that (spelled incorrectly, but who cares, it's math class)Now we multiply by a power of ten, so the divisor is a whole number. The following step is to divide by calculating how many times 25 equals 105. I realize it was stolen from the question, but whatever. So there was the explanation; I realize I didn't answer the entire problem, but I didn't have to; it wasn't in the cards.

3v + 7v + 9v =3 v+7 v+9 v= ​

Answers

Answer:

I cant help you

Step-bBecause i just c

y-step explanation:

According to a 2014 Pew Research poll, 58% of Americans believe in Hell. Suppose a random sample of 100 Americans is obtained and the number of Americans who believe in Hell is recorded. Can this binomial experiment be approximated using a normal distribution? Be sure to demonstrate your conclusion numerically.

Answers

Testing the conditions, we get that [tex]np = 58 \geq 10[/tex] and [tex]n(1 - p) = 42 \geq 10[/tex], thus, this binomial experiment can be approximated using a normal distribution.

For each person sampled, there are only two possible outcomes. Either they believe in Hell, or they do not. The probability of a person believing in hell is independent of any other person, which means that the binomial distribution is used to solve this question.

Binomial distribution:

Probability of x successes on n trials, with p probability.

If [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex], it can be approximated to the normal distribution.

In this problem:

Sample of size 100, thus [tex]n = 100[/tex].58% believe in Hell, thus [tex]p = 0.58[/tex].

Then

[tex]np = 100(0.58) = 58 \geq 10[/tex]

[tex]n(1 - p) = 100(0.42) = 42 \geq 10[/tex]

[tex]np = 58 \geq 10[/tex] and [tex]n(1 - p) = 42 \geq 10[/tex], thus, this binomial experiment can be approximated using a normal distribution.

A similar problem is given at https://brainly.com/question/24261244

What is the value sinθ?




12/13


13/5


5/12


5/13

Answers

Answer:

12/13

Step-by-step explanation:

I got a 100% on the test

The trigonometric function sin is the ratio of perpendicular to hypotenuse thus sinθ = 5/13.

What is a trigonometric function?

The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.

The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.

As per the given right angle triangle,

By sine function.

sinθ = perpendicular/hypotenuse

sinθ = 5/13

Hence "The trigonometric function sin is the ratio of perpendicular to hypotenuse thus sinθ = 5/13".

For more information about the trigonometric function,

https://brainly.com/question/14746686

#SPJ2

Jaden goes to dinner with his family. Their total bill comes to $52.25. They received
great service, so they decide to leave a 20% tip. How much should they leave for a
tip?
$16.12
$1.05
$10.45
$2.61

Answers

Answer:  $10.45  (choice C)

Work Shown:

20% = 20/100 = 0.20

20% of 52.25 = 0.20*52.25 = 10.45

side note: The total cost, including the tip, is 52.25+10.45 = 62.70 dollars

Anyone can solve this for me??

Answers

Answer:

15.25 is the better.

Step-by-step explanation:

you don't ounces divided by money.

NO LINKS!!!
Find the coordinates of point on the directed segment from (1,6) to (-2,-3) that divides it into a ratio of 5:1.
a. (-1.5,-1.5)
b. (1.5, 1.5)
c. (-1,-1)
d. (-2.5, -3.5)

Answers

Answer:

A. (-1.5, -1.5)

Step-by-step explanation:

Find the coordinates:

x = 1 + 5/6(- 2 - 1) = 1 - 5/2 = -1.5y = 6 + 5/6(-3 - 6) = 6 - 15/2 = -1.5

Correct choice is A

the differentiation of x^4 + y^4=0 is..?​

Answers

Answer:

I am doinnnnnmngggg gggg

how to solve 5 divided by 2545

Answers

2545 divided by 5 is 509

. A store is going to mark down all of their items by 33%. The cost of a computer you really want is $750. How much will the computer get marked down?

Answers

Answer:

$247.50

Step-by-step explanation:

33/100x750=247.50

Since 33% in a fraction is 33/100, use that x 750 and you will get how much the computer gets marked down.

Hope this helps! Thanks.

The table below shows the cost for a factory to produce mid-sized cars.Based on the information in the table, how much does it cost the factory to produce each car?
A.
$10,206.00
B.
$15,309.00
C.
$5,103.00
D.
$2,552.00

Answers

Answer:

B

Step-by-step explanation:

because you are looking for the car that cost the most

how to find root hair

Answers

I'll proceed by evaluating total length and surface area by scanned images. For measurements, I suggest to use winrhizo or any similar software. In this case the most important thing to think about is to use the appropiate acquisition parameters, I mean, to set a good resolution during scanning. Pixels of the aquired image should be smaller than root hairs diameter. Therefore, let me try to suggest you a good acquisition resolution. Making a quick research, it seems that hair root diameters range between 0,012 and 0,017 mm, so I suggest a resolution that will give a pixel dimension of 0,002 mm. Root hair diameters should be composed by 6-8 pixels, that is enough for winrhizo measurements. Resolution is measured in dpi, so in "dots/pixel per inch". A inch is 25,4 mm. We need pixels with a diameter of 0,002 mm, so in 25,4 mm we found 12700 pixels. That means 12700 dpi. It's a very high resolution, you need a good scanner and much space in your computer.

sin⁻¹(-[tex]-\frac{\sqrt{3} }{2}[/tex]

Answers

Answer:

240,300

[tex] \frac{4\pi}{3} . \: \: \frac{5\pi}{3} [/tex]

Help, What is the volume of the concrete piece?

Answers

Answer:

72,000

Step-by-step explanation:

multiply everything

Answer: 1,215 in ^ 3

Volume is length x width x height.
I would split the figure into two different parts.

(In the picture I drew a line)

So no let’s find the volume of both shapes.

The fist one is 8 x 5 x 19

You get 19 as the height because the 9 and the 10 need to be added together to get the height of the shape.

8 x 5 = 45

45 x 19 = 855

Now let’s find the volume of shape #2

20 x 8 x 9

20 x 8 = 40

40 x 9 = 360

Now we have the volume of the shape split into two parts so we need to add them together.

855 + 360 = 1,215

I think that’s how you do it. I haven’t done this in a while
Other Questions
Read the excerpt from White Fang.The four Indians laughed more loudly, while even the man who had been bitten began to laugh. They surrounded [White Fang] and laughed at him, while he wailed out his terror and his hurt. In the midst of it, he heard something. The Indians heard it, too. But the cub knew what it was, and with a last, long wail that had in it more of triumph than grief, he ceased his noise and waited for the coming of his mother, of his ferocious and indomitable mother who fought and killed all things and was never afraid. She was snarling as she ran. She had heard the cry of her cub and was dashing to save him.Which best states White Fangs perspective in the excerpt?He is angry at the men and feeling protective of his mother. He is afraid of the men and relieved to hear his mother coming.He is unafraid of the men and amused by his mothers snarling. He is curious about the men and afraid of disappointing his mother. Find the difference. Simplify the answer if possible.15 9/15 - 11 1/3A) 26 10/18B) 4 4/15C) -4 4/15D) 4 8/12 6 (31 + 163 72)6 +2= Please help me solve this ASAP please! please help :((Which of the following atoms has the largest radius?1. Na2. H3. Ar4. P 5. F 6. AI Please can someone write an essay "The Roles of Technology in Educating The African Youths" Helppp A local office supply store charges 18 to set up their business card printing machine with the design and $0.15 in materials per business card to print Which key idea does Zitkala-Sa develop in School Days of an Indian Girl? please help!I can't solve for m, g, h, or k What is the rate of return when 35 shares of Stock A, purchased for $20/share, are sold for $815? The commission on the sale is $6. Rate of Return = [?] % Give your answer as a percent rounded to the nearest tenth Ms. Dirr is selling her car to her sister. The original price of the car was $24,179 andeach year the car decreasing (goes down) by $3000. Write a function rule where C =value of the car and y = number of yearsO C = 3000 - 24179yO C = 24179 - 3000yO C = 3000 + 24179yOC - 24179 + 3000y helpppppooppppppppikkkk which excel feature prevents you from having to type the same thing over and over? Write the null and alternative hypothesis which would pertain to a hypothesis test described in each scenario last year politicians average 2000 trouble hours this year with an election occurring it is expected that they will travel more hours qu o chuyn ng ca vt l ng thng? what effects did the emphasis on individuals have on painters 3x^2-24x+48 pls help me please someone HELP I NEED TO GO TO BED SOON PLEASE GIVE ME ANSWER PLEASEE a) Describe in words the pattern relationship.b) Write a rule to describe the pattern shown.c) If the table had an input of 7, what would be the output?d) If the table had an output of 31, what would be the input? Find an equivalent system of equations for the following system:2x + 4y = 45x + 5y = 5A. 2x + 4y = 4 3x + y = 1B. 2x + 4y = 4 7x + 5y = 1C. 2x + 4y = 4 7x y = 5D. 2x + 4y = 4 7x y = 1 1. how does martin luther king jr. fit into the big picture of history?2. what is martin luther king jrs. historical significance?