[tex]\lbrack\frac{144q^2}{m^6p^4}\rbrack^{}[/tex]
Explanation
Let's remember some properties ofthe fractions ans exponents,
[tex]\begin{gathered} a^{-n}=\frac{1}{a^n} \\ (\frac{a}{b})^n=\frac{a^n}{b^n} \\ (ab)^n=a^nb^n \\ (a^n)^m=a^{m\cdot n} \end{gathered}[/tex]
so
Step 1
[tex]\lbrack\frac{4p^{-2}q}{3^{-1}m^3}\rbrack^2[/tex]
reduce by using the properties
[tex]\begin{gathered} \lbrack\frac{4p^{-2}q}{3^{-1}m^3}\rbrack^2 \\ \lbrack\frac{4q}{3^{-1}m^3p^2}\rbrack^2 \\ \lbrack\frac{3^1\cdot4q}{m^3p^2}\rbrack^2 \\ \lbrack\frac{12q}{m^3p^2}\rbrack^2 \\ \lbrack\frac{144q^2}{m^{3\cdot2}p^{2\cdot2}}\rbrack^{} \\ \lbrack\frac{144q^2}{m^6p^4}\rbrack^{} \end{gathered}[/tex]
therefore, the answer is
[tex]\lbrack\frac{144q^2}{m^6p^4}\rbrack^{}[/tex]
I hope this helps you
