Which of the following expressions is equivalent to (2^3)^2?

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Question: Which of the following expressions is equivalent to (2^3)^2?

Options:

Correct Answer: 2^6

Solution:

Using the power of a power property, (a^m)^n = a^(m*n), we get 2^(3*2) = 2^6.

Which of the following expressions is equivalent to (2^3)^2?

Which of the following expressions is equivalent to (2^3)^2?

Step 1: Identify the expression we need to simplify, which is (2^3)^2.
Step 2: Recall the power of a power property, which states that (a^m)^n = a^(m*n).
Step 3: In our case, a is 2, m is 3, and n is 2.
Step 4: Apply the property: (2^3)^2 becomes 2^(3*2).
Step 5: Calculate the exponent: 3*2 equals 6.
Step 6: Therefore, (2^3)^2 simplifies to 2^6.

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