# GMAT Math : Understanding exponents

## Example Questions

### Example Question #1124 : Problem Solving Questions

Give the sum in scientific notation:

Explanation:

Rewrite the second addend as follows:

This is not in scientific notation; we adjust as follows:

### Example Question #1125 : Problem Solving Questions

Give the quotient in scientific notation:

Explanation:

Since 0.9375 does not fall in the range  , we adjust the answer as follows:

### Example Question #23 : Exponents

Give the difference in scientific notation:

Explanation:

Rewrite the second addend as follows:

### Example Question #24 : Exponents

Express the product in scientific notation:

Explanation:

Since 40 does not fall inside the rangle , we adjust the answer as follows:

### Example Question #21 : Understanding Exponents

If , what does  equal?

Explanation:

We can use the fact that  to see that

Since , we have

.

### Example Question #26 : Exponents

Simplify:

Explanation:

Use the properties of exponents as follows:

### Example Question #21 : Exponents

Solve for

The equation has no solution.

Explanation:

The left and right sides of the equation have the same base, so we can equate the exponents and solve:

### Example Question #1131 : Problem Solving Questions

Which of the following is equal to   ?

Explanation:

We'll need to remember a few logarithmic properties to answer this question:

Now we can use these same rules to rewrite the log in question:

### Example Question #1132 : Problem Solving Questions

Simplify the following expression:

.

Explanation:

We start by simplifying the expression on the top. Let's add the exponents inside the parentheses and then multiply by the exponent outside of the parentheses.

Then we substract the denominator exponent form the numerator exponent:

### Example Question #1133 : Problem Solving Questions

Simplify the following:

.