1. Laws of Exponents: Dividing Monomials Division Rules for Exponents

2. 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?

3. 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, = x m – n xmxm xnxn When dividing like bases, subtract the exponents. Examples: = x 5 – 3 x5x5 x3x3 = x2x2 1.

4. Laws of Exponents: Dividing Monomials Examples Use the properties of exponents to simplify expressions containing fractions. = Subtract the exponents for the x (7 -1= 6) Subtract the exponents for the y (3 -2 = 1) x7y3x7y3 xy 2 x6yx6y 4x 5 6x 2 = Reduce the coefficients. Subtract the exponent of the variables. 2x 3 3 2. 3.

5. Laws of Exponents: Dividing Monomials Do These Together 4. x6x6 x4x4 = x 2 5. x3y7x3y7 xy 4 = x 2 y 3 6. 5x 7 y 3 z 6 15x 3 yz 4 = x4y2z2x4y2z2 3 7. 10x 3 y 4 6xy 4 = 5x 2 3

6. Laws of Exponents: Dividing Monomials TRY THESE 8. x8x8 x3x3 = x 5 9. x4y7x4y7 x4y2x4y2 = y 5 10. 6x 4 y 6 z 8 2x 2 y 3 z 5 = 3x 2 y 3 z 3 11. 18x 5 y 9 12x 3 y 3 = 3x 2 y 6 2

7. 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 3 7 to determine the value of 3 0 Zero Property of Exponents A nonzero number to the zero power is 1:

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

9. 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 a n to determine the value of a -n

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

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

12. Laws of Exponents: Dividing Monomials