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* a^n=a^(m+n)`

The expression becomes,

`(-5r^7s^(-9))(8r^(-7)s^(-1))=-40* r^(7+(-7))* s^(-9+(-1))`

Simplifying the expression,

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

Applying the identity,

`\begin{gathered} a^0=1 \\ a^(-n)=(1)/(a^n) \end{gathered}`

After substituting the identity the expression is,

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

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