College Algebra Problem?

Question

solve: x^3/2=125
Must show work.

Answer 1

when you have an exponient of an exponient it multiplies.

So if you have x^(3/2)^(2/3) it equals x^1.

Therefore the key to this problem is to raise both sides to the 2/3 power.

x^(3/2)^(2/3)=125^(2/3)
x=5^2
x=25

Answer 2

In order to solve this problem:

(x³)/2 = 125

First, multiply by 2 on both sides to get x on one side of the equation:

(x³)/2 = 125
= (x³)/2 * 2 = 125 * 2
= x³ = 250

Now, cube root both sides in order to solve for x. A cube root is like a square root, except that you must find three numbers (instead of two) that multiply together to get a certain number. For example:

y^(1/3) = cube root of y = b (where (b * b * b) = y)

Therefore:

x³ = 250
= (x³)^(1/3) = 250^(1/3)
= x = about 6.3

This is your answer: x = about 6.3.

Otherwise, if you meant:

x^(3/2) = 125

Then the answer would be different.

In order to solve this, raise both sides of the equation to the power of 2/3. This will solve for x:

x^(3/2) = 125
= (x^(3/2))^(2/3) = 125 ^ (2/3)
= x = 25

These are the two possible answer: x = 25 or x = about 6.3, depending on what you meant by the question.

Hope this helps!

Answer 3

well...

we have x^(3/2) = 125

let's raise both sides to the power of 2/3 .

( x^(3/2) ) ^ (2/3) = 125 ^ (2/3)

Raising x ^ (3/2) by (2/3) multiplies those exponents.

In other words...(3/2) * (2/3), which equals 1

So we have x = 125 ^ (2/3)

This can be rewritten as (125 ^ (1/3) ) ^ 2

125 ^ (1/3) is the same as saying the cube root of 125, which happens to be 5 (since 5 * 5 * 5 = 125).

So we are left with 5 ^ 2 which equals 25.

Answer 4

is this 1/2 of x^3 or x^(3/2) ?

Answer 5

The question is asking: The square root of what number cubed would be 125? Work backwards.

So we square 125 to get 15625. Then, we gotta get the cube root of that to get the answer: 25.

Answer 6

√x³ = 125
x³ = 125²
x•x•x=(5•5•5)²
x•x•x=5•5•5•5•5•5
x=5•5
x=25

Answer 7

What does the ^ mean?