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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