Final answer:
To find the value of (2²)³, we perform the exponentiation inside the first set of parentheses and raise the result to the power of 3. For (2³)², we perform the exponentiation inside the second set of parentheses and raise the result to the power of 2. Both expressions have the same results because we multiply the exponents in both cases.
Step-by-step explanation:
To find the value of (2²)³, we need to follow the order of operations: first, we perform the exponentiation inside the first set of parentheses, which gives us 2² = 4. Then, we raise the result to the power of 3, so 4³ = 4 × 4 × 4 = 64.
To find the value of (2³)², we again follow the order of operations: first, we perform the exponentiation inside the second set of parentheses, which gives us 2³ = 8. Then, we raise the result to the power of 2, so 8² = 8 × 8 = 64.
The results of both expressions are 64, which means that (2²)³ is equal to (2³)². This is because when we raise a power to another power, we multiply the exponents. In this case, both expressions have the same exponentiation operation, so the results are the same.