GRE Math : Algebra

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Example Questions

Example Question #31 : Algebra

Solve for

$2^{x+1}=128$

Possible Answers:

Correct answer:

Explanation:

Recall that 128=2^7 .

With same base, we can write this equation:

x+1=7 .

By subtracting on both sides, x=6 .

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Example Question #2 : Exponents And Rational Numbers

Solve for .

$2^{x^2+4}=32$

Possible Answers:

-1, 1

Correct answer:

-1, 1

Explanation:

Since 32=2^5 we can rewrite the expression.

With same base, let's set up an equation of x^2+4=5 .

By subtracting on both sides, we get x^2=1 .

Take the square root of both sides we get BOTH and .

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Example Question #8 : Exponents And Rational Numbers

Solve for .

5^x=25^4

Possible Answers:

Correct answer:

Explanation:

They don't have the same base, however: 25=5^2 .

Then 25^4=(5^2)^4 . You would multiply the and the instead of adding.

$2\cdot 4=8$ .

x=8

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Example Question #9 : Exponents And Rational Numbers

Solve for .

$4^{2x}=16^6$

Possible Answers:

Correct answer:

Explanation:

There are two ways to go about this.

Method

They don't have the same bases however: 16=4^2 . Then 16^6=(4^2)^6

You would multiply the and the instead of adding. We have $2\cdot 6=2x$

Divide on both sides to get x=6 .

Method :

We can change the base from to 16.

$4^{2x}=(4^2)^x=16^x$

This is the basic property of the product of power exponents.

We have the same base so basically x=6 .

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Example Question #10 : Exponents And Rational Numbers

Solve for .

1024^x=2

Possible Answers:

$\frac{1}{10}$

$-\frac{1}{10}$

Correct answer:

$\frac{1}{10}$

Explanation:

Since we can write $1024^x=(2^{10})^x$ .

With same base we can set up an equation of 10x=1

Divide both sides by and we get $x=\frac{1}{10}$ .

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Example Question #11 : Exponents And Rational Numbers

Solve for .

$1024^x=\frac{1}{2}$

Possible Answers:

$\frac{1}{10}$

$-\frac{1}{10}$

Correct answer:

$-\frac{1}{10}$

Explanation:

$1024^x=(2^{10})^x$

We still don't have the same base however: $2=\frac{1}{2}^{-1}$

Then,

$1024^x=(2^{10})^x=\left[\left(\frac{1}{2}\right)^{-1}\right]^{10x}$ .

With same base we can set up an equation of -10x=1 .

Divide both sides by and we get $x=\frac{-1}{10}$ .

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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 answer cannot be determined from the information given.

Quantity B is greater.

The two quantities are equal.

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

Quantity B:

Possible Answers:

Quantity A is greater.

The relationship cannot be determined from the information given.

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 #13 : Exponents And Rational Numbers

$2^{-5}$

Possible Answers:

$-\frac{1}{32}$

$\frac{1}{32}$

Correct answer:

$\frac{1}{32}$

Explanation:

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

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

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Example Question #31 : Algebra

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

Possible Answers:

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

16^8

$4^{12}$

$2^{24}$

64^4

Correct answer:

16^8

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,

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

$2^{24}$

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

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GRE Math : Algebra

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #31 : Algebra

Example Question #2 : Exponents And Rational Numbers

Example Question #8 : Exponents And Rational Numbers

Example Question #9 : Exponents And Rational Numbers

Example Question #10 : Exponents And Rational Numbers

Example Question #11 : Exponents And Rational Numbers

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 #13 : Exponents And Rational Numbers

Example Question #31 : Algebra

All GRE Math Resources

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