Question

38133)=3"3-5What is the value of n?SHOW HINT

Answer 1

The value of n is;

`n=13`

Step-by-step explanation:

Given the equation;

`(\frac{3^{8^{}}}{3^(-5)})=3^n`

Applying the rules of indices;

`(1)/(x^m)=x^(-m)`

we have;

`\begin{gathered} (\frac{3^{8^{}}}{3^(-5)})=3^n \\ (3^{8^{}}\cdot3^(-(-5)))=3^n \\ (3^{8^{}}\cdot3^5)=3^n \\ 3^(8+5)=3^n \\ 3^(13)=3^n \end{gathered}`

Therefore, since the base are equal, then the value of n is;

`n=13`