Question

for what value of n does

Answer 1

Answer:

Option (4). 1

Step-by-step explanation:

Given expression is $\frac{(216)^{n-2}}{(\frac{1}{36})^{3n}}$= 216

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

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

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

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

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

$(6)^{3n-6+6n}$ = $(6)^3$

$(6)^{9n-6}=(6)^3$

9n - 6 = 3

9n = 3 + 6

9n = 9

n = 1

Option (4) will be the answer.