Question

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

Answer 1

$\frac{1}{57.76r^{8}s^{10}}$

Explanation

let's remember some rules to operate exponents

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

so

Step 1

given

$(\frac{5}{8}r^{-1})^0(-7.6r^4s^5)^{-2}$

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

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

b) now, to expand apply the second rule

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

therefore, the answer is

$\frac{1}{57.76r^8s^{10}}$

I hope this helps you