1. Negative Exponents Chapter 8 section 3

2. Let’s Review Exponents… Multiplying with exponents: When you multiply by the base, the exponent in the result increases by one. ex. 10³ x 10=10⁴

3. Let’s Review Exponents Dividing with exponents: When you divide by the base, the exponent in the result decreases by one. ex. 10ˉ² ÷ 10=10ˉ³

4. Negative Exponents Not all exponents are positive. Some exponents are negative. Look at the pattern below to see the value of 10³=1000 10²=100 10¹=10 10°=1 10¯¹=? 10¯²=?

5. Negative Exponents Continued 10³=1000 10²=100 10¹=10 10°=1 10¯¹=.1 10¯²=.01

6. METHOD 1: Quotient of Powers We can use the Quotient of Powers rule and the definition of power to simplify the expression below: x³ = x³ˉ⁵= x x⁵ Because 3 minus 5 equals -2…so it simplifies to x ˉ²

7. METHOD 2: Definition of Power x³ = xxx x⁵ xxxxx The variables (x) in red will cancel out with each other. So, what do we have left? = ___1____ OR 1 xx x²

8. Simplify The Expression Write 10ˉ³ using positive exponents So…we write 10ˉ³ as __1__ 10³ We can write this as __1__ OR 0.001 100

9. Your Turn! 1.2ˉ⁴2. 10ˉ² 1__1_ 2⁴ 10²_1_ 16 100

10. Let’s Simplify! EXAMPLE: xyˉ² = = x _1_ y² *Y goes on bottom b/c of the negative exponent! = _1_ y²

11. Exponents w/Division Simplify the following: a³bˉ⁴ = a³m²n¹⁰ = n⁸ b⁴ m⁵n² m³

12. Your Turn Simplify each expression mn¯³ = m n³ x⁴y x² x²y⁵ = y⁴

13. HOMEWORK Pg.350: 15-45 ODD