Chapter A.1, Problem 63E

Solution

Simplify the exponential expression.

  $y$ .

Given:

The given expression is $\frac{{(x^9{y}^6)}^{1/3}}{{(x^6{y}^2)}^{1/2}}$ .

Concept Used:

• Exponential expressions are just a way to write powers in short form. The exponent indicates the number of times the base is used as a factor.

Calculation:

The given expression is $\frac{{(x^9{y}^6)}^{1/3}}{{(x^6{y}^2)}^{1/2}}$ .

  $\begin{array}{c}\frac{{(x^9{y}^6)}^{1/3}}{{(x^6{y}^2)}^{1/2}}=\frac{{(x^9)}^{1/3}{(y^6)}^{1/3}}{{(x^6)}^{1/2}{(y^2)}^{1/2}}\\ =\frac{x^3{y}^2}{x^{3}y}\\ =y\end{array}$

Thus after simplifying the given expression $\frac{{(x^9{y}^6)}^{1/3}}{{(x^6{y}^2)}^{1/2}}$ is $y$ .