Chapter 7.3, Problem 25PPE

To determine

To simplify: The expression ${\left(36g^4\right)}^{-\frac{1}{2}}$ .

Answer to Problem 25PPE

The required answer is $\frac{1}{6g^2}$ .

Explanation of Solution

Given information:

The given expression ${\left(36g^4\right)}^{-\frac{1}{2}}$ .

Calculation:

  $\begin{array}{l}={\left(36g^4\right)}^{-\frac{1}{2}}\\ ={36}^{-\frac{1}{2}}{\left(g^4\right)}^{-\frac{1}{2}}\end{array}$

(Raise each factor to the second power)

  $\begin{array}{l}={36}^{-\frac{1}{2}}{g}^{4\cdot \left(-\frac{1}{2}\right)}\\ ={36}^{-\frac{1}{2}}{g}^{-2}\end{array}$

(Multiply the exponents of a power raised to a power)

  $=\frac{1}{6}\cdot \frac{1}{g^2}$

(The expression using only positive exponents)

  $=\frac{1}{6g^2}$

(Simplify)