GRE Quantitative Reasoning - How to find a rational number from an exponent

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

Quantity B:

Quantity B is greater.

Quantity A is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

Explanation

(–1) 137= –1

–1 < 0

(–1) odd # always equals –1.

(–1) even # always equals +1.

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

43 34

Quantity B is greater.

Quantity A is greater.

The two quantities are equal.

The answer cannot be determined from the information given.

Explanation

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

43 is 4 * 4 * 4 = 64

34 is 3 * 3 * 3 * 3 = 81

Therefore, Quantity B is greater.

$2^{-5}$

$\frac{1}{32}$

$-\frac{1}{32}$

Explanation

Anything raised to negative power means over the base raised to the postive exponent.

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

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

$2^{24}$

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

$4^{12}$

Explanation

Let's all convert the bases to .

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

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

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

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

Therefore,

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

$2^{24}$

is not like the answers so this is the correct answer.

Simplify

$2^{10}+2^9$

$2^9\cdot 3$

$2^{19}$

$2^{10}$

$2^{18}\cdot 3$

$2^{10}\cdot 3$

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 .

We have .

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

How to find a rational number from an exponent

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