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

Study concepts, example questions & explanations for GRE Math

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Example Questions

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

 

find x

8x=2x+6

Possible Answers:

-1

4

2

2 or -1

3

Correct answer:

3

Explanation:

8 = 23

(23)x = 23x

 

23x = 2x+6  <- when the bases are the same, you can set the exponents equal to each other and solve for x

3x=x+6

2x=6

x=3

Example Question #2 : Exponents And Rational Numbers

Compare 3^{6} and 27^{2}.

Possible Answers:

3^{6} = 27^{2}

3^{6} > 27^{2}

3^{6} < 27^{2}

The relationship cannot be determined from the information given.

Correct answer:

3^{6} = 27^{2}

Explanation:

First rewrite the two expressions so that they have the same base, and then compare their exponents.

27 = 3^{3}   

27^2 = (3^{3})^2

Combine exponents by multiplying: (3^{3})^2 = 3^6

This is the same as the first given expression, so the two expressions are equal.

Example Question #3 : Exponents And Rational Numbers

Solve for 

Possible Answers:

Correct answer:

Explanation:

 can be written as  

Since there is a common base of , we can say

  or 

Example Question #4 : Exponents And Rational Numbers

Solve for .

 

Possible Answers:

Correct answer:

Explanation:

The basees don't match.

However: 

 thus we can rewrite the expression as .

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

So, 

Example Question #5 : Exponents And Rational Numbers

Solve for .

Possible Answers:

Correct answer:

Explanation:

The bases don't match.

However: 

 and we recognize that .

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

.  

 

Example Question #31 : Algebra

Solve for 

Possible Answers:

Correct answer:

Explanation:

Recall that 

With same base, we can write this equation: 

By subtracting  on both sides, 

 

Example Question #31 : Gre Quantitative Reasoning

Solve for .

Possible Answers:

Correct answer:

Explanation:

Since  we can rewrite the expression.

With same base, let's set up an equation of .

By subtracting  on both sides, we get .

Take the square root of both sides we get BOTH  and 

Example Question #7 : How To Find An Exponent From A Rational Number

Solve for .

Possible Answers:

Correct answer:

Explanation:

They don't have the same base, however: .

Then . You would multiply the  and the  instead of adding.

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

Solve for .

Possible Answers:

Correct answer:

Explanation:

There are two ways to go about this.

Method 

They don't have the same bases however: . Then 

You would multiply the  and the  instead of adding. We have 

Divide  on both sides to get .

 

Method :

We can change the base from  to 

 

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

We have the same base so basically 

Example Question #3 : How To Find An Exponent From A Rational Number

Solve for .

Possible Answers:

Correct answer:

Explanation:

Since we can write 

With same base we can set up an equation of  

Divide both sides by  and we get 

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