This document discusses the rules for simplifying expressions with variables that have exponents. 1) When adding or subtracting terms with the same base and exponent, you combine the coefficients and keep the base and exponent the same. 2) When multiplying terms, you add the exponents and multiply the coefficients. 3) When dividing terms, you subtract the bottom exponent from the top exponent and divide the coefficients.

1. Exponent properties

2. Do Now x 5 (x 3 ) x 8 / x 5 x 3 + x 3 7x 2 – 3x 2 (x 2 ) 3 x 8 x 3 2x 3 4x 2 x 6

3. Adding and Subtracting Variables with Exponents When adding or subtracting variables with exponents, variables must have the same base and exponent.

4. Examples x 2 + x 2 = 2x 2 2. 5x 2 - x 2 = 4x 2 Notice how the base and exponent always stay the same. You only change the coefficient when adding or subtracting. Both x x 2 + x 2 + x 2 + x 2 + x 2 – x 2 = 4x 2

5. Multiplying Variables with Exponents When multiplying variables with exponents, you must add the exponents together. Coefficients are multiplied.

6. Examples 1. x 4 (x 3 ) = x 7 2. 5x 7 (x 2 ) = 5x 9 x·x·x·x·x·x·x = x 7 5x 7+2 = 5x 9

7. To divide variables with exponents, you must subtract the bottom exponent from the top exponent, and divide the coefficients. Dividing Variables With Exponents

8. Examples 2x 3 2. x 2 = x -3 = 1 x 2 x 5 x 3 2 • x • x • x = 2x x•x

9. Powers of Powers When simplifying powers of powers, you must distribute the exponent to the coefficient and variable’s exponent. Multiply the exponents.

10. Examples (2a 2 ) 3 2 3 (a 2 ) 3 8a 2(3) 8a 6

11. Examples (cont.) * Remember to only distribute the exponent to what is in the parentheses. Example: 5(x 4 ) 3 = 5x 12

12. Exit Slip Simplify. 1. 7x 3 -3x 3 2. 6x 2 3x 3 3.(4x 5 ) 2 4. x 2 +2x 2 5.8x 3 (4x 3 ) 4x 3 2x 2 3. 16x 10 4. 3x 2 5. 32x 6