SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} a) \\ (10^2)\text{ }^{-3\text{ }}=\text{ 10}^{(\text{ 2 x -3 \rparen }}=\text{ 10}^{-6} \\ Hence\text{, \lparen10}^2)^{-3}=\text{ 10}^{-6} \end{gathered}[/tex][tex]\begin{gathered} b)\text{ } \\ (\text{ 3}^{-3})^2=\text{ 3}^{(-3\text{ x 2\rparen}}=3^{-6} \\ Hence,\text{ \lparen3}^{-3})^2=\text{ 3}^{-6} \end{gathered}[/tex][tex]\begin{gathered} \text{ c\rparen }3^{-5\text{ }}\times\text{ 4}^{-5}=\text{ \lparen3}\times\text{4 \rparen}^{-5}=\text{ \lparen12\rparen}^{-5} \\ Hence,\text{ 3}^{-5}\times\text{ 4}^{-5}=\text{ \lparen12\rparen}^{-5} \end{gathered}[/tex][tex]\begin{gathered} d) \\ 2^5\times\text{ 3}^{-5}=\text{ 2}^5\text{ x }\frac{1}{3^5}=\frac{2^5}{3^5}=\text{ \lparen}\frac{2}{3})^5 \\ Hence,\text{ 2}^5\text{ x 3}^{-5}=\text{ \lparen }\frac{2}{3})^5 \end{gathered}[/tex]
