 # Integer Exponents

Related Topics:
Common Core for Mathematics
More Math Lessons for Grade 8

Videos, examples, solutions, and lessons to help Grade 8 students know and apply the properties of integer exponents to generate equivalent numerical expressions.
For example, 32 × 3–5 = 3–3 = 1/33 = 1/27.

Common Core: 8.EE.1

### Suggested Learning Targets

• I can explain why a zero exponent produces a value of one.
• I can explain how a number raised to an exponent of -1 is the reciprocal of that number.
• I can explain the properties of integer exponents to generate equivalent numerical expressions.

1. Multiplying Exponents of the same base
For example, 32 x 3-5 = 1/33 = 1/27

2. Dividing Exponents of the same base
For example, 32/ 3-1 = 1/33 = 1/27

3. Expand an exponent by another exponent
For example (22)3 = 64

8.EE.1-1 - Rules of Exponents
Product of Powers Property
To multiply powers with the same base, add their exponents.
Examples:
1. Lake Powell, the reservoir behind the Glen Canyon Dam in Arizona can hold about 1012 cubic feet of water when full. There are about 1027 water molecules in 1 cubic foot of water. About how many water molecules can the reservoir hold?

2. 3x•5x2 =

Quotient of Powers Property
To divide powers with same base, subtract the exponent of the denominator from the exponent of the numerator.
Example:
Simplify (3m5•m2)/6m3
Know and apply the properties of integer exponents to generate equivalent expressions (8.EE.1)
Why exponents are used, how to simplify same base numbers with exponents, and how to show equivalent expressions to bases that contain negative exponents?
Exponents - The Power of Zero

Applying exponents rules
Examples:
Apply the rules to the problems:
1. (105)(103) =
2. 3x7•5x4 =
3. (a2)(a5)(a4) =
4. (y-7)(y5) =

Examples:
Apply the rules to the problems:
1. (103)2 =
2. (4a2)4 =
3. (x3)2(x2)6 =
4. (5m4)-3 =
Simplify expressions involving negative exponents - 8.EE.1
How to simplify simple expressions involving negative exponents?
Examples:
Simplify the following by first removing the negative signs and then removing the exponents
1. 4-2
2. 5-3
3. 2-4
4. 3-1

Divide the following, leaving the answers with exponents.
1. 56 ÷ 52
2. 87/83

Simplify and perform the operation indicated.
1. 23 × 32
2. 62 ÷ 23

Simplify and perform the operation indicated.
1. 32 + 23
2. 52 + 33
3. 42 + 93
4. 23 - 22 