GRE Math : How to find a rational number from an exponent

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Example Questions

Example Question #1 : How To Find A Rational Number From An Exponent

Quantitative Comparison: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given.

Quantity A Quantity B

4³3⁴

Possible Answers:

The two quantities are equal.

The answer cannot be determined from the information given.

Quantity A is greater.

Quantity B is greater.

Correct answer:

Quantity B is greater.

Explanation:

In order to determine the relationship between the quantities, solve each quantity.

4³is 4 * 4 * 4 = 64

3⁴ is 3 * 3 * 3 * 3 = 81

Therefore, Quantity B is greater.

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Example Question #2 : How To Find A Rational Number From An Exponent

Quantity A: $(-1)^{137}$ $\displaystyle (-1)^{137}$

Quantity B: $\displaystyle 0$

Possible Answers:

The relationship cannot be determined from the information given.

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

Correct answer:

Quantity B is greater.

Explanation:

(–1) ¹³⁷= –1

–1 < 0

(–1) ^{odd #} always equals –1.

(–1) ^{even #} always equals +1.

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Example Question #33 : Algebra

$2^{-5}$ $\displaystyle 2^{-5}$

Possible Answers:

$\displaystyle 2$

$\frac{1}{32}$ $\displaystyle \frac{1}{32}$

$\displaystyle 32$

$\displaystyle -32$

$-\frac{1}{32}$ $\displaystyle -\frac{1}{32}$

Correct answer:

$\frac{1}{32}$ $\displaystyle \frac{1}{32}$

Explanation:

Anything raised to negative power means $\displaystyle 1$ over the base raised to the postive exponent.

$2^{-5}=\frac{1}{2^5}=\frac{1}{32}$ $\displaystyle 2^{-5}=\frac{1}{2^5}=\frac{1}{32}$

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Example Question #15 : Exponents And Rational Numbers

Which of the following is not the same as the others?

Possible Answers:

16^8 $\displaystyle 16^8$

$2^{24}$ $\displaystyle 2^{24}$

$(\frac{1}{2})^{^{-24}}$ $\displaystyle (\frac{1}{2})^{^{-24}}$

64^4 $\displaystyle 64^4$

$4^{12}$ $\displaystyle 4^{12}$

Correct answer:

16^8 $\displaystyle 16^8$

Explanation:

Let's all convert the bases to $\displaystyle 2$.

$4^{12}=[2^2]^{12}=2^{24}$ $\displaystyle 4^{12}=[2^2]^{12}=2^{24}$

$64^4=(2^6)^4=2^{24}$ $\displaystyle 64^4=(2^6)^4=2^{24}$

$16^8=[2^4]^8=2^{32}$ $\displaystyle 16^8=[2^4]^8=2^{32}$

$\left(\frac{1}{2}\right)^{^{-24}}$ $\displaystyle \left(\frac{1}{2}\right)^{^{-24}}$ This one may be intimidating but $2=\frac{1}{2}^{-1}$ $\displaystyle 2=\frac{1}{2}^{-1}$.

Therefore,

$\left(\left[\frac{1}{2}\right]^{-24}\right)^{-1}=2^{24}$ $\displaystyle \left(\left[\frac{1}{2}\right]^{-24}\right)^{-1}=2^{24}$

$2^{24}$ $\displaystyle 2^{24}$

16^8 $\displaystyle 16^8$ is not like the answers so this is the correct answer.

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Example Question #41 : Exponents

Simplify

$2^{10}+2^9$ $\displaystyle 2^{10}+2^9$

Possible Answers:

$2^{18}\cdot 3$ $\displaystyle 2^{18}\cdot 3$

$2^9\cdot 3$ $\displaystyle 2^9\cdot 3$

$2^{10}$ $\displaystyle 2^{10}$

$2^{19}$ $\displaystyle 2^{19}$

$2^{10}\cdot 3$ $\displaystyle 2^{10}\cdot 3$

Correct answer:

$2^9\cdot 3$ $\displaystyle 2^9\cdot 3$

Explanation:

Whenever you see lots of multiplication (e.g. exponents, which are notation for repetitive multiplication) separated by addition or subtraction, a common way to transform the expression is to factor out common terms on either side of the + or - sign. That allows you to create more multiplication, which is helpful in reducing fractions or in reducing the addition/subtraction to numbers you can quickly calculate by hand as you'll see here.

So let's factor a 2^9 $\displaystyle 2^9$.

We have $\displaystyle 2^9(2+1)$.

And you'll see that the addition inside parentheses becomes quite manageable, leading to the final answer of $2^9\cdot 3$ $\displaystyle 2^9\cdot 3$.

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GRE Math : How to find a rational number from an exponent

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 : How To Find A Rational Number From An Exponent

Example Question #2 : How To Find A Rational Number From An Exponent

Example Question #33 : Algebra

Example Question #15 : Exponents And Rational Numbers

Example Question #41 : Exponents

All GRE Math Resources

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