GMAT Math : Understanding exponents

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #84 : Algebra

Simplify:

Possible Answers:

Unable to simplify

Correct answer:

Explanation:

The first thing we must do is distribute the exponents outside of the parentheses across each expression (remembering of course that exponents set to another exponent are multiplied).

 

The last step is to follow the rules of exponent addition/subtraction:

 and 

Therefore:

  

Example Question #61 : Exponents

Which of the following is true if  ?

Possible Answers:

The equation has no solution.

Correct answer:

Explanation:

To answer this question, note that 

and 

.

Therefore, since

it follows that 

and 

.

Example Question #62 : Exponents

Solve for :

Possible Answers:

The equation has no solution.

Correct answer:

Explanation:

Rewrite both sides as powers of 2 using the exponent rules as follows:

Since powers of the same base are equal, set the exponents equal to each other:

Example Question #1161 : Problem Solving Questions

Solve for :

Possible Answers:

The equation has no solution.

Correct answer:

Explanation:

Rewrite both sides as powers of 3 using the exponent rules as follows:

Since powers of the same base are equal, set the exponents equal to each other:

Example Question #83 : Algebra

Solve for :

Possible Answers:

The equation has no solution.

Correct answer:

Explanation:

Rewrite all expressions as powers of 2, and use the exponent rules as follows:

Since powers of the same base are equal, set the exponents equal to each other:

Example Question #84 : Algebra

Solve for :

Possible Answers:

The equation has no solution.

Correct answer:

Explanation:

Rewrite the first expression to get:

Example Question #65 : Exponents

Solve for :

Possible Answers:

The equation has no solution.

Correct answer:

The equation has no solution.

Explanation:

Rewrite both sides as powers of 2 using the exponent rules as follows:

Since powers of the same base are equal, set the exponents equal to each other:

This is identically false, so the equation has no solution.

Example Question #66 : Exponents

Simplify:

Possible Answers:

Correct answer:

Explanation:

The first step is two distribute the squared exponent across the numerator:

We can then subtract the denominator's exponents from the numerator's leaving us with the answer:

Example Question #61 : Understanding Exponents

The first two terms of a geometric sequence are  and , in that order. Give the tenth term.

(Assume  is positive.)

Possible Answers:

Correct answer:

Explanation:

The common ratio of the geometric sequence can be found by dividing the second term by the first:

The tenth term of the sequence is therefore

Example Question #68 : Exponents

Express  in terms of .

Possible Answers:

Correct answer:

Explanation:

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