Chapter A.1, Problem 60E

Solution

Simplify the exponential expression.

  $\frac{x^3}{y^4}$ .

Given:

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

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 ${\left(\frac{x^{1/2}}{y^{2/3}}\right)}^6$ .

  $\begin{array}{c}{\left(\frac{x^{1/2}}{y^{2/3}}\right)}^6=\frac{{(x^{1/2})}^6}{{(y^{2/3})}^6}\\ =\frac{x^{\frac{6}{2}}}{y^{\frac{12}{3}}}\\ =\frac{x^3}{y^4}\end{array}$

Thus after simplifying the given expression ${\left(\frac{x^{1/2}}{y^{2/3}}\right)}^6$ is $\frac{x^3}{y^4}$ .