Question

A student simplified the rational expression

Answer 1

Answer:

The student solved the rational expression incorrectly.

Step-by-step explanation:

Given :  Steps of a student who solved a given rational expression.

We have to check whether he is correct or not.

Consider the given expression

$\left(\frac{x^{\frac{2}{5}}\cdot x^{\frac{4}{5}}}{x^{\frac{2}{5}}}\right)^{\frac{1}{2}}$

Applying exponent rule ,$\:a^b\cdot \:a^c=a^{b+c}$

we have,

$x^{\frac{2}{5}}x^{\frac{4}{5}}=\:x^{\frac{2}{5}+\frac{4}{5}}=\:x^{\frac{6}{5}}$

$=x^{\frac{6}{5}}$

Thus, the expression becomes,

$=\frac{x^{\frac{6}{5}}}{x^{\frac{2}{5}}}$

Apply exponent rule , $\quad \frac{x^a}{x^b}\:=\:x^{a-b}$

$\frac{x^{\frac{6}{5}}}{x^{\frac{2}{5}}}=x^{\frac{6}{5}-\frac{2}{5}}=x^{\frac{4}{5}}$

$=\left(x^{\frac{4}{5}}\right)^{\frac{1}{2}}$

Applying exponent rule $\left(a^b\right)^c=a^{bc},$

$=x^{\frac{4}{5}\cdot \frac{1}{2}}=x^{\frac{2}{5}}$

Thus, $\left(\frac{x^{\frac{2}{5}}x^{\frac{4}{5}}}{x^{\frac{2}{5}}}\right)^{\frac{1}{2}}=x^{\frac{2}{5}}$

Thus, The student solved the rational expression incorrectly.

                                                                                                         

Answer 2

(x^3)^1/2 is NOT CORRECT
It is:
= (x^(6/5 - 2/5) )^1/2
= (x^4^5)^1/2
= x^2/5