What is the value of the expression \frac{3^8 + 3^8 + 3^8}{3^4}? — GMAT

What is the value of the expression $\frac{3^8 + 3^8 + 3^8}{3^4}$ ?

3^5

The correct answer is

3^5

. Adding three identical values

3^8 + 3^8 + 3^8

is equivalent to

3 \times 3^8

, which equals

3^9

. Dividing

3^9

3^4

gives

3^{9-4} = 3^5

Simplify the numerator by combining like terms

3^8 + 3^8 + 3^8 = 3 \cdot 3^8 = 3^1 \cdot 3^8 = 3^{1+8} = 3^9

Repeated addition of

3

identical terms is equivalent to multiplying one term by

3

Apply the quotient rule for exponents

\frac{3^9}{3^4} = 3^{9-4} = 3^5

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

Combining like exponential terms using multiplication rules and applying the quotient rule for exponents

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