Question

For what value of n does startfraction 216 superscript n minus 2 baseline over (startfraction 1 over 36 endfraction superscript 3 n?

Answer 1

They are written in term of power to the base of a function. The value of n that will make both expression equal is 2/9

Exponential expression

They are written in term of power to the base of a function. Given the expression below:

$216^{n-2}=\frac{1}{36}^{3n}$

This can be further simplified as:

$6^3^{n-2}=(6^{-2})^{3n}\\6^{3n-2}=6^{-6n}$

Cancel the base to have:

3n-2 = -6n
3n+6n = 2

9n = 2

n = 2/9

Hence the value of n that will make both expression equal is 2/9

Learn more on indices here: https://brainly.com/question/10339517

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