What is the value of (2^3 + 2^3)^2? — GMAT

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

The correct answer is

2^8

Combining the terms inside the parentheses gives

2^3 + 2^3 = 2 \cdot 2^3 = 2^4

. Squaring

2^4

using the power rule

(a^m)^n = a^{m \cdot n}

produces

2^{4 \cdot 2} = 2^8

Simplify the expression inside the parentheses

2^3 + 2^3 = 2 \cdot (2^3) = 2^1 \cdot 2^3 = 2^4

Adding two identical terms is equivalent to multiplying the term by 2, which allows combining powers of the same base.

Apply the power of a power exponent rule to the outer square

(2^4)^2 = 2^{4 \times 2} = 2^8

When raising a power to another power, multiply the exponents:

(a^m)^n = a^{m \cdot n}

Combining like exponential terms and applying power rules

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