What is the value of \frac{2^7 + 2^7}{2^4}? — GRE General Test

What is the value of $\frac{2^7 + 2^7}{2^4}$ ?

Combining the numerator yields

2^7 + 2^7 = 2(2^7) = 2^8

. Dividing

2^8

2^4

using the quotient rule gives

2^{8-4} = 2^4 = 16

Simplify the numerator by factoring out common terms

2^7 + 2^7 = 2 \times 2^7 = 2^{1+7} = 2^8

Adding two identical exponential terms is equivalent to multiplying one term by 2.

Apply the quotient rule of exponents

\frac{2^8}{2^4} = 2^{8-4} = 2^4

When dividing exponential expressions with the same base, subtract the exponent of the denominator from the exponent of the numerator.

Evaluate the power

2^4 = 16

Compute the numerical value of 2 raised to the 4th power.

Combining like exponential terms and applying the quotient rule of exponents.

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