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GRE Math : How to find a ratio of exponents

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Example Questions

Example Question #21 : Algebra

Quantitative Comparison

Quantity A: $4^5 * 4^{-3}$

Quantity B: $\frac{4^5}{4^{-3}}$

Possible Answers:

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

Correct answer:

Quantity B is greater.

Explanation:

In Quantity A, we add the exponents because the operation is multiplication, so 4⁵ * 4^–3= 4^5+(–3) = 4². In Quantity B, we subtract the exponents because the operation is division, so 4⁵ / 4^–³= 4^5–(–3) = 4⁸. We don't have to finish multiplying out the exponents to see that Quantity B is greater.

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Example Question #21 : Algebra

If and are both rational numbers and $4^{m} = 8^{n}$ , what is $\frac{m}{n}$ ?

Possible Answers:

$\frac{2}{1}$

$\frac{4}{1}$

$\frac{3}{2}$

$\frac{5}{3}$

Correct answer:

$\frac{3}{2}$

Explanation:

This question is asking you for the ratio of m to n. To figure it out, the easiest way is to figure out when 4 to an exponent equals 8 to an exponent. The easiest way to do that is to list the first few results of 4 to an exponent and 8 to an exponent and check to see if any match up, before resorting to more drastic means of finding a formula.

$4^{1} = 4, 4^{2} = 16, 4^{3} = 64, 4^{4} = 256, 4^{5} = 1024$

$8^{1}=8, 8^{2} = 64, 8^{3} = 512, 8^{4} = 4096, 8^{5} = 32768$

And, would you look at that. $4^{3}= 8^{2}$ . Therefore, $\frac{m}{n} = \frac{3}{2}$ .

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GRE Math : How to find a ratio of exponents

Study concepts, example questions & explanations for GRE Math

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Example Question #21 : Algebra

Example Question #21 : Algebra

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