Chapter 7.3, Problem 96PFA

To determine

To solve the given equation.

Answer to Problem 96PFA

  $j=2^5$

Explanation of Solution

Given:

Equation: $j=\sqrt[5]{32\times 32\times 32\times 32\times 32}$

Formula used:

Exponent rule:

  $x^{\frac{a}{b}}=\sqrt[b]{x^a}$

Calculation:

Consider the given equation,

  $\Rightarrow j=\sqrt[5]{32\times 32\times 32\times 32\times 32}$

The equation can be simplified as,

  $\begin{array}{c}j=\sqrt[5]{{32}^5}\\ ={32}^{\frac{5}{5}}[\because x^{\frac{a}{b}}=\sqrt[b]{x^a}]\\ ={32}^1\\ =32\end{array}$

Also, 32 can be written as $2^5$

Hence,

  $j=2^5$

Conclusion:

The solution to the given equation is $j=2^5.$