# GMAT Math : Understanding exponents

## Example Questions

### Example Question #84 : Algebra

Simplify:

Unable to simplify

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).

and

Therefore:

### Example Question #61 : Exponents

Which of the following is true if  ?

The equation has no solution.

Explanation:

To answer this question, note that

and

.

Therefore, since

it follows that

and

.

### Example Question #62 : Exponents

Solve for :

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:

### Example Question #1161 : Problem Solving Questions

Solve for :

The equation has no solution.

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 :

The equation has no solution.

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 :

The equation has no solution.

Explanation:

Rewrite the first expression to get:

### Example Question #65 : Exponents

Solve for :

The equation has no solution.

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:

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.)

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 .