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 m–n = x 1. xn When dividing like bases, subtract the exponents. 5 x Examples: 5– 3 2 x = x 3

Laws of Exponents: Dividing Monomials Examples Use the properties of exponents to simplify expressions containing fractions. 7 y 3 x 6 y 2. x = xy 2 3 5 2 x 4 x 3. 6 x 2 = 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. x 6 2 = x x 4 5. x 3 y 7 = x 2 y 3 xy 4 6. 5 x 7 y 3 z 6 7. 15 x 3 yz 4 10 x 3 y 4 6 xy 4 x 4 y 2 z 2 = 3 = 5 x 2 3

Laws of Exponents: Dividing Monomials TRY THESE 8. x 8 5 = x x 3 9. x 4 y 7 x 4 y 2 = y 5 2 y 3 z 3 4 y 6 z 8 3 x 6 x 10. = 2 x 2 y 3 z 5 11. 18 x 5 y 9 12 x 3 y 3 = 3 x 2 y 6 2

Laws of Exponents: Dividing Monomials By applying the product of powers property to the following example, we find that: Zero Property of Exponents We can then divide both sides of the equation by 37 to determine the value of 30 A nonzero number to the zero power is 1:

Laws of Exponents: Dividing Monomials Evaluate the following expressions. Solutions

Laws of Exponents: Dividing Monomials By applying the product of powers property to the following example, we find that: We can then divide both sides of the equation by an to determine the value of a-n

Laws of Exponents: Dividing Monomials Evaluate the following expressions. Solutions Rewrite the following expressions using positive exponents.

Laws of Exponents: Dividing Monomials 1) Evaluate the following expressions. 2) Rewrite the following expressions with positive exponents.

Laws of Exponents: Dividing Monomials

Laws of Exponents: Dividing Monomials