Exponent properties

Do Now1. x5(x3)

2. x8 / x5

3. x3 + x3

4. 7x2 – 3x2

5. (x2)3

1. x8

2. x3

3. 2x3

4. 4x2

5. x6

Adding and Subtracting Variables

with ExponentsWhen adding or subtractingvariables with exponents, variables must have the same base and exponent.

Examples1. x2 + x2 = 2x2

2. 5x2 - x2 = 4x2

• Notice how the base and exponent always stay the same. You only change the coefficient when adding or subtracting.

Both x

x2 + x2 + x2 + x2 + x2 – x2 = 4x2

Multiplying Variables with Exponents

When multiplying variables withexponents, you must add the

exponentstogether. Coefficients are multiplied.

Examples

1. x4(x3) = x7

2. 5x7(x2) = 5x9

x·x·x·x·x·x·x = x7

5x7+2 = 5x9

To divide variables with exponents, you must subtract the bottom

exponent from the top exponent, and divide the coefficients.

Dividing Variables With Exponents

Examples1. 2x3 2. x2 = x-3 = 1

x2 x5 x3

2 • x • x • x = 2x

x•x

Powers of PowersWhen simplifying powers of powers, you must distribute the exponent to

the coefficient and variable’s exponent. Multiply the exponents.

Examples(2a2)3

23(a2)3

8a2(3)

8a6

Examples (cont.)

*Remember to only distribute the exponent to what is in the

parentheses.Example:

5(x4)3 = 5x12

Exit SlipSimplify.

1. 7x3-3x3

2. 6x2

3x3

3.(4x5)2

4. x2+2x2

5.8x3(4x3)

1.4x3

2.2x2

3. 16x10

4. 3x2

5. 32x6