Exponents for 6th Grade Math Students

Exponents for 6th Graders

What's an Exponent?

Exponents have two parts: a base and a power. For example, in the exponent 4^3, four is the base and three is the power. Exponents tell you to find the base to a certain power, which means to multiply the base a certain number of times. For the exponent 4^3, you'd multiply four three times, like this: 4 x 4 x 4. The solution would be 64, since 4 x 4 = 16 and 16 x 4 = 64. Here are a few more examples:

2^2 = 2 x 2 = 4

3^4 = 3 x 3 x 3 x 3 = 81

5^3 = 5 x 5 x 5 = 125

Special Rules

Here are a few special exponent rules to keep in mind:

1. One raised to any power equals one, since one times itself always equals one (1^543 = 1).

2. Any number to the 'zero' power equals one (3^0 = 1).

3. A number to the first power equals itself (7^1 = 7).

Exponent Expressions

In 6th grade, you'll also learn to simplify expressions with exponents, like 3^3 ÷ 9. For a problem like this, simplify the exponent first, and then complete the operation. For instance, here's how you'd solve this problem:

3^3 ÷ 9

= 3 x 3 x 3 ÷ 9

= 27 ÷ 9

= 3

Practice Problems

Here are some exponent practice problems. After you've completed them, use the key below to check your answers.

1. 8^1

2. 1^8

3. 5^2

4. 2^5

5. 74^0

6. 5 + 6^3

7. 7^2 - 7

8. 3 x 3^1

9. 24 ÷ 2^3

10. 1 ÷ 4^2

Answer Key

1. Since any number to the first power equals itself, 8^1 = 8.

2. One to any power equals itself, so 1^8 = 1.

3. The exponent 5^2 equals 5 x 5, which equals 25.

4. Since 2 x 2 x 2 x 2 x 2 = 32, 2^5 = 32.

5. Any number to the zero power equals one, so 74^0 = 1.

6. To solve 5 + 6^3, first simplify 6^3. Since 6 x 6 x 6 = 216, you can add five to this to get 221 (5 + 216 = 221).

7. For 7^2 - 7, the product of 7 x 7 is 49. Then, 49 - 7 = 42.

8. Begin solving 3 x 3^1 by simplifying 3^1 to three. Then, multiply three by itself to get nine (3 x 3 = 9).

9. Since 2^3 = 2 x 2 x 2 = 8, 24 ÷ 2^3 = 3.

10. The answer to 1 ÷ 4^2 is a fraction. The exponent 4^2 = 4 x 4 = 16, and 1/16 cannot be simplified further.