Question

A student simplified the rational expression

using the steps shown.
(x^2/5 • x^4/5 / x^2/5)^1/2 = (x^6/5/x^2/5)^1/2=(x^3)^1/2=x^3/2
Is the answer correct? Explain.

Answer 1

`\textbf{No, the answer is not correct }`.

Explanation:

The student didn't use the quotient of powers property correctly. Instead of subtracting, the student divided the exponents within the parenthesis. So, x to the two-fifths power is the correct simplified form.

`((x^(2/5)* x^(4/5) )/(x^(2/5) ) )`

`=((x^(6/5) )/(x^(2/5) ) )^(1/2)`

`=x^(6/5-2/5) )^(1/2)`

`=(x^(4/5) )^(1/2) =x^(2/5)`

OAmalOHopeO

Answer 2

Does the answer help you?