Question

What exponent would make the two expressions equivalent (3³)^x÷3²⁴?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To make the two expressions equivalent, we need to make the base of the first expression, 3³, equal to the base of the second expression, 3²⁴.

We have the equation 3³ = 3²⁴.

Since the bases are equal, we can equate the exponents:
3 = 24x.

To solve for x, we divide both sides of the equation by 24:
3/24 = x.

Simplifying the left side of the equation gives us:
1/8 = x.

Therefore, the exponent x that would make the two expressions equivalent is 1/8.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To make the two expressions equivalent, we need to find the exponent that makes them equal.

We have the expression (3³)^x ÷ 3²⁴.

We can simplify this expression by applying the exponent rules. Since both 3³ and 3²⁴ have the base 3, we can rewrite the expression as (3³)^(x-24).

For the expressions to be equal, the exponents must be equal. So we set x - 24 equal to 1:

x - 24 = 1

To solve for x, we add 24 to both sides of the equation:

x = 1 + 24

Therefore, the exponent that would make the two expressions equivalent is x = 25.