Question

(3^2)^6 = _____

A) 3^-4
B) 3^4
C) 3^8
D) 3^12

Answer 1

The correct answer is option D). 3^12

Explanation:

Points to remember

Identities

(xᵃ)ᵇ = xᵃᵇ

xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾

xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ⁾

It is given that (3^2)^6

To find the correct option

(3^2)^6 can be written as, (3²)⁶

By using above identities,

(3²)⁶ = 3⁽² ˣ ⁶⁾

= 3¹²

Therefore the correct answer is option D). 3^12

Answer 2

Hello!

The answer is:

The correct option is:

D)
`(3^(2))^(6)=3^(12)`

Why?

To solve the problem, we need to remember the power of a power property, it's defined by the following way:

`(a^(m))^(n)=a^(m*n)`

When we have a power of a power, we must keep the base and then, the new exponent will be the product between the two original exponents.

So, we are given the expression:

`(3^(2))^(6)`

Then, calculating we have:

`(3^(2))^(6)=3^(2*6)=3^(12)`

Hence, we have that the correct option is:

D)
`(3^(2))^(6)=3^(12)`