Chapter 7.2, Problem 45P

Simplify each expression.

$\frac{1}{x^4\cdot x^{-9}}$

To determine

To simplify the expression $\frac{1}{x^4.x^{-9}}$

Answer to Problem 45P

  $\frac{1}{x^4.x^{-9}}=x^5$

Explanation of Solution

Given information :

Given expression $\frac{1}{x^4.x^{-9}}$

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

  $\begin{array}{l}\text{Now consider}\frac{1}{x^4.x^{-9}}=\frac{1}{x^{4-9}}fromrule(i)\\ =\frac{1}{x^{-5}}\\ =x^5\text{since}\frac{1}{x^{-5}}=x^5\\ \therefore \frac{1}{x^4.x^{-9}}=x^5\end{array}$

Hence, $\frac{1}{x^4.x^{-9}}=x^5$