What is the value of (2^3)^2?

What is the value of (2^3)^2?

• A. 8
• B. 16
• C. 32
• D. 64

Answer: (D)

To find the value of \((2^3)^2\), you can apply the laws of exponents. Specifically, when raising a power to another power, you multiply the exponents. Starting with the expression: \[ (2^3)^2 = 2^{3 \cdot 2} = 2^6 \] Now, calculate \(2^6\). This means multiplying 2 by itself six times: \[ 2^6 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \] Calculating this step by step: - \(2 \times 2 = 4\) - \(4 \times 2 = 8\) - \(8 \times 2 = 16\) - \(16 \times 2 = 32\) - \(32 \times 2 = 64\) Thus, \(2^6 = 64\). Therefore, the value of \((2^3)^2\) is 64.

To find the value of ((2^3)^2), you can apply the laws of exponents. Specifically, when raising a power to another power, you multiply the exponents.

Starting with the expression:

[

(2^3)^2 = 2^{3 \cdot 2} = 2^6

]

Now, calculate (2^6). This means multiplying 2 by itself six times:

[

2^6 = 2 \times 2 \times 2 \times 2 \times 2 \times 2

]

Calculating this step by step:

• (2 \times 2 = 4)

• (4 \times 2 = 8)

• (8 \times 2 = 16)

• (16 \times 2 = 32)

• (32 \times 2 = 64)

Thus, (2^6 = 64). Therefore, the value of ((2^3)^2) is 64.