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# Exponents Help

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By McGraw-Hill Professional
Updated on Sep 7, 2011

## Exponents

When the same number is multiplied by itself, the indicated product can be written in exponential notation . For example, 3×3 can be written as 3 2 ; there the 3 is called the base and the 2 is called the exponent . Also,

3×3×3 = 3 3

3×3×3×3 = 3 4

3×3×3×3×3 = 3 5 , etc.

3 2 is read as "three squared" or "three to the second power," 3 3 is read as "three cubed" or "three to the third power," 3 4 is read as "three to the fourth power," etc.

Math Note: When no exponent is written with a number, it is assumed to be one. For example, 3 = 3 1 .

Find 5 3 .

#### Solution 1

5 3 = 5× 5× 5× = 125

Find 2 8 .

#### Solution 2

2 8 = 2× 2× 2× 2× 2×2×2×2 = 256

### Negative Quantities and Exponents

Exponents can be used with negative numbers as well. For example, (-8) 3 means (-8)×(-8)×(-8). Notice that in the case of negative numbers, the integer must be enclosed in parentheses. When the sign is not enclosed in parentheses, it is not raised to the power. For example, -8 3 means -8·8·8.

Find (-5) 4 .

#### Solution 1

(-5) 4 =(-5)(-5)(-5)(-5)= 625

Find 5 4 .

#### Solution 2

-5 4 = -5×5×5×5 = -625

### Exponents Practice Problems

#### Practice

Find:

1. 7 4

2. 3 7

3. 5 2

4. 2 1

5. (-3) 4

6. (-6) 3

7. (-4) 5

8. -4 6

9. -7 4

10. -9 3

1. 2401

2. 2187

3. 25

4. 2

5. 81

6. -216

7. -1024

8. -4096

9. -2401

10. -729

More practice problems for this concept can be found at: Integers Practice Test.

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