Question

How do you simplify `(5x ^ { 3} ) ( 2x ) ^ { - 3}`?

Answer 1

`5/8`

Explanation:

Remember the PEMDAS. (Parenthesis, exponents, multiplication and division, addition and subtraction.)

You need to do `(2x)^-3` first, which is `1/ (2x)^3=>1/(8x^3)`
Now, multiply this by `5x^3`, which is `(5x^3)/(8x^3)`

Simplify the fraction. The numerator and the denominator shares `x^3` as its factor.

Therefore, our answer is `5/8`

Answer 2

Remember `u^(-a) = 1/u^a`. See explanation.

Explanation:

We will solve his both for the second term as written (`(2x)^(-3)`) , and for `2x^(-3)`. This second option has the exponent applied solely to the variable.

First, recall that by definition for any expression `u` and exponent `a`, `u^(-a)= 1/u^a`.

This means that..

`(2x)^(-3)=1/(2x)^3= 1/(8x^3)`

Multiplying by the First term then gives us...

`(5x^3)/(8x^3)=5/8`

If the second term was instead only applying the exponent to the variable, the 2 would remain in the numerator:

`2(x^(-3)) = 2/x^3`

In which case we instead have

`5x^3 × 2(x^(-3)) = 5x^3 * 2/x^3 = 2* = 10`