GRE-Style: Exponent Comparison

GRE Quantitative · Axiom Academy

EXAMPLE GRE-Style: Comparing 32^ 2/5 and 4 A quantitative comparison combining a root and a power on a fractional exponent. This is a GRE-style Quantitative Comparison. Compare the quantity in Column A to the quantity in Column B. Nice work — you compared a fractional-exponent expression to a whole number by breaking it into a root and a power. Rewrite the exponent: For a^ m/n , take the n th root first, then raise the result to the m power: . Roots first is easier: Finding 32^ 1/5 = 2 first keeps the numbers small — squaring 32 directly first would be far messier. Result: 32^ 2/5 = 4 , so the two columns are equal. Watch for this pattern on the GRE: a fractional exponent is almost always faster to evaluate as "root, then power" rather than trying to compute the power first.

This is the written version of the interactive lesson above. See the full GRE Quantitative course.