Chapter 9.1, Problem 2MRE

To determine

The positive exponents.

Answer to Problem 2MRE

The required exponent in positive form is $\frac{b^8}{a^{12}}$ .

Explanation of Solution

Given:

  ${\left(a^{-3}{b}^2\right)}^4$

Calculation:

Solving exponents using property of exponents:

  $\begin{array}{l}{\left(a^{-3}{b}^2\right)}^4\\ =a^{-3\times 4}{b}^{2\times 4}\\ =a^{-12}{b}^8\\ =\frac{b^8}{a^{12}}\end{array}$

The value is $\frac{b^8}{a^{12}}$ .