Chapter 7.9, Problem 54WE

To determine

To calculate: The simplified form of the expression $\frac{d^{-3}}{d^{-5}}$ .

Answer to Problem 54WE

The simplified form of the expression $\frac{d^{-3}}{d^{-5}}$ is $d^2$ .

Explanation of Solution

Given information:

The expression $\frac{d^{-3}}{d^{-5}}$ .

Formula used:

Law of exponent for quotient of powers is $a^m÷a^n=a^{m-n}$ where a is a nonzero integers and n and m are positive integers.

The expression $a^{-n}$ is expressed as $\frac{1}{a^n}$ where a is a nonzero real number and n is a positive integer.

Calculation:

Consider the expression $\frac{d^{-3}}{d^{-5}}$ .

Recall that law of exponent for quotient of powers is $a^m÷a^n=a^{m-n}$ where a is a nonzero integers and n and m are positive integers.

Apply it,

  $\begin{array}{c}\frac{d^{-3}}{d^{-5}}=d^{-3-\left(-5\right)}\\ =d^{-3+5}\\ =d^2\end{array}$

Thus, the simplified form of the expression $\frac{d^{-3}}{d^{-5}}$ is $d^2$ .