Question

What is the value of 3 to the power 2 over 3 to the power 4? A. 1 over 81 B. 1 over 27 C. 1 over 9 D. 1 over 3

Answer 1

Answer:

Option C is correct.

Step-by-step explanation:

Given Expression:

$\frac{3^2}{3^4}$

We need to find Value of given expression.

Consider,

$\frac{3^2}{3^4}$

$\implies3^{2-4}$

$\implies3^{-2}$

$\implies\frac{1}{9}$

Therefore, Option C is correct.

Answer 2

One way you could solve this is to just multiply the top and bottom out so that you get 9/81, reducing it by 9/9 to get 1/9 or option C.
Another way would be to do $3^{(2-4)}$ since dividing numbers with exponents would be subtracting the bottom exponent from the top exponent, provided that the base number (in this case 3) is the same for both. For this method, you would get $3^{-2}$, which is equal to 1/9 or .1 repeating, the same answer that you'd get with the first method.