# Laws of Exponents: Dividing Monomials Division Rules for Laws of Exponents: Dividing Monomials Division Rules for Exponents Laws of Exponents: Dividing Monomials Division Rules of Exponents Essential Questions How do I divide powers with the same bases? How do I simplify expressions with negative and zero exponents? Laws of Exponents: Dividing Monomials Rules and Properties Quotient-of-Powers Property For all nonzero real numbers x and all integers m and n, where m > n, xm mn = x 1. xn Examples: When dividing like bases, subtract the exponents. x5 53 2 x = x = x3 Laws of Exponents: Dividing Monomials Examples Use the properties of exponents to simplify expressions containing fractions. 7 3 x y 2. = x6y xy 2 3 5 2x

4x 3. 6x2 = 3 Subtract the exponents for the x (7 -1= 6) Subtract the exponents for the y (3 -2 = 1) Reduce the coefficients. Subtract the exponent of the variables. Laws of Exponents: Dividing Monomials Do These Together 4. x6 2 4 = x x 5. x3y7 = x2y3 xy4 6. 5x7y3z6 15x3yz4 7. 10x3y4 6xy 4 x4y2z2 = 3 = 5x2 3 Laws of Exponents: Dividing Monomials TRY THESE 8. x8 5 3 = x x

9. x4y7 x4y2 = y5 4 6 8 6x yz 10. 2x2y3z5 11. 18x5y9 12x3y3 = 3x2y3z3 3x2y6 = 2 Laws of Exponents: Dividing Monomials 0 3 3 By applying the product of powers property to the following example, we find that: 3 0 3 7 3 0 7 3 7 We can then divide both

sides of the equation by 37 to determine the value of 30 3 7 3 1 7 7 3 3 7 0 Zero Property of Exponents A nonzero number to the zero power is 1: a 0 1, a 0 Laws of Exponents: Dividing Monomials Evaluate the following expressions. A . 7 0 2 B. 4 4 2 0 C. 2 5

3 D . 3 8 0 E. 0 0 Solutions A . 1 2 B. 4 4 2 4 0 0 C. 2 5 3 1 D . 1 E. 0 0 is u n d e fin e d . 1 125 125 Laws of Exponents: Dividing Monomials By applying the product of powers property to the following example, we find that:

a n a n a n ( n ) a 0 1 We can then divide both sides of the equation by an to determine the value of a-n a n a n a n a n a a n a -n 1 n

1 n a 1 a n is th e re c ip ro c a l n of a : a n 1 a n , a 0 Laws of Exponents: Dividing Monomials Evaluate the following expressions. A . 3 2 1 B. 4 -3 Rewrite the following expressions using positive exponents. A . 5x Solutions A . 3 B.

2 1 4 3 B. A . 5x 1 3 1 9 4 4 4 3 64 B . 3 5 a b a -3 b -5 1 5

2 a b a 1 3 5 3 x 5 x b 4 5 4 Laws of Exponents: Dividing Monomials 1) Evaluate the following expressions. A. - 3 5 0 B. 3 2 3 C. 9 4 9 7 D .

2 2 4 E. 1 3 2 120 2) Rewrite the following expressions with positive exponents. A. y 6 B . 7c 4 2s3 C . 2 r D . (5a ) 3 E. 1 4 3 x Laws of Exponents: Dividing Monomials A . B. 3 2 3 3 5 0

D . 1 2 2 4 22 4 4 3 2 4 256 3 3 8 24 C. 9 4 9 7 9 47 93 243 E. 1 3 2 12 0

2 3 1 9 Laws of Exponents: Dividing Monomials A . y 6 B . 7c 4 C. r 3 2 D . 6 y c E. 3x 1 4 3 1 125a 3 4

14 2s3 r 2 3 2 1 3 3 5 a 4 4 2s r 1 7 c 5 a 3 1 7 2s 1 4 x x x4 81 4