Question

Apply all relevant properties of exponents to simplify the following expression. Enter your answer as an expression without negative exponents

Answer 1

Given,

The expression is,

$(-5r^7s^{-9})(8r^{-7}s^{-1})$

Applying the identity,

$a^m\times a^n=a^{m+n}$

The expression becomes,

$(-5r^7s^{-9})(8r^{-7}s^{-1})=-40\times r^{7+(-7)}\times s^{-9+(-1)}$

Simplifying the expression,

$\begin{gathered} (-5r^7s^{-9})(8r^{-7}s^{-1})=-40\times r^{7-7}\times s^{-9-1} \\ =-40\times r^0\times s^{-10} \end{gathered}$

Applying the identity,

$\begin{gathered} a^0=1 \\ a^{-n}=\frac{1}{a^n} \end{gathered}$

After substituting the identity the expression is,

$\begin{gathered} (-5r^7s^{-9})(8r^{-7}s^{-1})=-40\times r^0\times s^{-10} \\ =-40\times1^{}\times\frac{1}{s^{10}} \\ =-\frac{40}{s^{10}} \end{gathered}$

Hence, the simplified answer is -40/(s^10).