How to find a ratio of exponents - GRE Quantitative Reasoning

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Question

Quantitative Comparison

Quantity A:

Quantity B:

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Answer

In Quantity A, we add the exponents because the operation is multiplication, so 45 * 4–3 = 45+(–3) = 42. In Quantity B, we subtract the exponents because the operation is division, so 45 / 4–3 = 45–(–3) = 48. We don't have to finish multiplying out the exponents to see that Quantity B is greater.

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