Chapter 7.2, Problem 32P

Complete each equation.

$d^7\cdot d^{-13}\cdot d^{-9}=d^{\square }$

To determine

To complete the equation $d^7.d^{-13}.d^{-9}=d^{\left[\right]}$

Answer to Problem 32P

  $d^7.d^{-13}.d^{-9}=d^{\left[-15\right]}$

Explanation of Solution

Given information :

Given equation $d^7.d^{-13}.d^{-9}=d^{\left[\right]}$

As we know that $\left(a^m\right)\left(a^n\right)=a^{m+n}\mathrm{........}\text{(i)}$

Let $x$ be the unknown value

Now consider $d^7.d^{-13}.d^{-9}=d^{\left[x\right]}$

  $\begin{array}{l}\Rightarrow d^{7-13-9}=d^x\\ \Rightarrow 7-13-9=x\\ \therefore x=-15\end{array}$

Hence, $d^7.d^{-13}.d^{-9}=d^{\left[-15\right]}$