Question

20 POINTS HELPPPPP

Answer 1

Answer:

n = 1

Step-by-step 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:

$\frac{(6^3)^{n-2}}{(\frac{1}{6^2})^{3n}}=216$

Now, we can write the denominator using the rule:

$a^b=\frac{1}{a^{-b}}$

So, it becomes:

$\frac{(6^3)^{n-2}}{(\frac{1}{6^2})^{3n}}=216\\\frac{(6^3)^{n-2}}{(6^{-2})^{3n}}=216$

Now, we can use the rule:

$(a^z)^b=a^{zb}$

So, we have:

$\frac{(6^3)^{n-2}}{(6^{-2})^{3n}}=216\\=\frac{6^{3n-6}}{6^{-6n}}=216$

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

$\frac{a^x}{a^y}=a^{x-y}$

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

Answer 2

Answer:

n = 1

Step-by-step explanation: