Question

20 POINTS HELPPPPP

For what value of n does StartFraction 216 Superscript n minus 2 Baseline Over (StartFraction 1 Over 36 EndFraction Superscript 3 n?

–3

Negative one-third

Five-ninths

1

Answer 1

n = 1

Explanation:

Answer 2

n = 1

Explanation:

We need to solve this equation for "n".

We first have to recognize the denominator and numerator as a "same" base number.

We know that 216 and 36 can be written as powers of 6. So, we write:

`((6^3)^(n-2))/(((1)/(6^2))^(3n))=216`

Now, we can write the denominator using the rule:

`a^b=(1)/(a^(-b))`

So, it becomes:

`((6^3)^(n-2))/(((1)/(6^2))^(3n))=216\\((6^3)^(n-2))/((6^(-2))^(3n))=216`

Now, we can use the rule:

`(a^z)^b=a^(zb)`

So, we have:

`((6^3)^(n-2))/((6^(-2))^(3n))=216\\=(6^(3n-6))/(6^(-6n))=216`

When we have same base, we can write it together using the identity:

`(a^x)/(a^y)=a^(x-y)`

Thus,

`6^((3n-6)-(-6n))=216`

Writing RHS as 6^3 and solving, we have:

`6^(3n-6+6n)=6^3\\6^(9n-6)=6^3\\9n-6=3\\9n=9\\n=1`

Thus,

n = 1