Question

Law of Exponents. Simplify each expression. Answers should be written with positive exponents.(-5p^6 times r^-9)^0

Answer 1

Given the expression:

`(-5p^6\cdot r^(-9))^0`

Simplifying using the law of exponents,

`\begin{gathered} (-5p^6\cdot r^(-9))^0=(-5* p^(-6)* r^(-9))^0 \\ \end{gathered}`

but

`a^(-b)=(1)/(a^b)`

thus, we have

`\begin{gathered} (-5* p^(-6)* r^(-9))^0=(-5*(1)/(p^6)*(1)/(r^9))^0 \\ =(-(5)/(p^6r^9))^0 \end{gathered}`

From the zero index law of exponents,

`a^0=1`

This implies that

`(-(5)/(p^6r^9))^0=1`

Hence, the solution to the expression is 1