Question

What exponent would make the two expressions equivalent: (3^3)^x = 3^24?

1. 8
2. 15
3. 21
4. 27

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the exponent that would make the two expressions equivalent, we can use the property of exponents which states that (a^b)^c = a^(b*c).

In this case, we have (3^3)^x = 3^24.

Using the property of exponents, we can rewrite the left side of the equation as 3^(3*x). Thus, we have 3^(3*x) = 3^24.

Now, since the bases are the same (3), we can set the exponents equal to each other. Therefore, we have 3*x = 24.

To solve for x, we divide both sides of the equation by 3: x = 24/3 = 8.

Therefore, the answer is 8.

Answer 2

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

To find the exponent that would make the two expressions equivalent, we can set the exponents equal to each other:

(3^3)^x = 3^24

Using the property of exponents, we can simplify the left side of the equation:

3^(3x) = 3^24

Now, since the bases are the same (which is 3), we can set the exponents equal to each other:

3x = 24

Dividing both sides of the equation by 3, we get:

x = 8

Therefore, the correct answer is 1. 8.

Answer 3

[AI-generated answer — Explain Bot]

To find the exponent that would make the two expressions equivalent, we need to use the property of exponents that states (a^m)^n = a^(m*n).

In this case, we have (3^3)^x = 3^24. Using the property mentioned above, we can write the equation as 3^(3*x) = 3^24.

Since the bases of both sides of the equation are equal (both are 3), the exponents must also be equal. Therefore, we can set up the equation 3*x = 24.

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

Simplifying the division gives us x = 8.

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

Hence, the answer is 1. 8.