# Exponents for 6th Grade Math Students

In 6th grade, you'll practice writing exponents and simplifying expressions with exponents. Read on for an explanation of this important middle school math skill, as well as ten practice problems!

### 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

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.
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