Question

Determine an equivalent algebraic monomial expression for each expression using the laws of exponents.

Answer 1

`(1)/(57.76r^(8)s^(10))`

Step-by-step explanation

let's remember some rules to operate exponents

`\begin{gathered} a^0=1 \\ (ab)^n=a^nb^n \\ a^(-n)=(1)/(a^n) \\ (a^n)(a^m)=(a^(m+n)) \\ (a^n)^m=a^(m*n) \end{gathered}`

so

Step 1

given

`((5)/(8)r^(-1))^0(-7.6r^4s^5)^(-2)`

a) the firs term is 1 because any number with exponent zero equals 1 ( first rule)

`\begin{gathered} ((5)/(8)r^(-1))^0(-7.6r^4s^5)^(-2) \\ ((5)/(8)r^(-1))^0=1\text{, hence} \\ (1)(-7.6r^4s^5)^(-2) \\ \begin{equation*} (-7.6r^4s^5)^(-2) \end{equation*} \end{gathered}`

b) now, to expand apply the second rule

`\begin{gathered} \begin{equation*} (-7.6r^4s^5)^(-2) \end{equation*} \\ (-7.6r^4s^5)^(-2)=(-7.6^(-2))(r^4)^(-2)(s^5)^(-2) \\ (-7.6r^4s^5)^(-2)=((-7.6)^(-2))(r^(4*-2))(s^(5*-2)) \\ (-7.6r^4s^5)^(-2)=(1)/((-7.6^()2))r^(-8)s^(-10) \\ (-7.6r^4s^5)^(-2)=(1)/(57.76r^8s^(10)) \end{gathered}`

therefore, the answer is

`(1)/(57.76r^8s^(10))`

I hope this helps you