Question

Rewrite each expression in an equivalent form with a single exponent.

Answer 1

Step 1:

In this question, we are given the following:

Step 2:

The details of the solution are as follows:

`\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}`
`\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}`
`\begin{gathered} \text{ c\rparen }3^{-5\text{ }}*\text{ 4}^(-5)=\text{ \lparen3}*\text{4 \rparen}^(-5)=\text{ \lparen12\rparen}^(-5) \\ Hence,\text{ 3}^(-5)*\text{ 4}^(-5)=\text{ \lparen12\rparen}^(-5) \end{gathered}`
`\begin{gathered} d) \\ 2^5*\text{ 3}^(-5)=\text{ 2}^5\text{ x }(1)/(3^5)=(2^5)/(3^5)=\text{ \lparen}(2)/(3))^5 \\ Hence,\text{ 2}^5\text{ x 3}^(-5)=\text{ \lparen }(2)/(3))^5 \end{gathered}`