Division Rules for Exponents

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?

Rules and Properties Quotient-of-Powers Property For all nonzero real numbers x and all integers m and n, where m > n, = xm – n xm xn When dividing like bases, subtract the exponents. 1. = x5 – 3 x5 x3 Examples: x2 =

Examples Use the properties of exponents to simplify expressions containing fractions. Subtract the exponents for the x (7 -1= 6) x7y3 xy 2 2. = x6y Subtract the exponents for the y (3 -2 = 1) Reduce the coefficients. 4x5 2x3 3. = 6x2 3 Subtract the exponent of the variables.

Do These Together x6 4. = x2 x4 x3y7 5. = x2y3 xy4 5x7y3z6 x4y2z2 6. = 7. = 3 6xy4

TRY THESE x8 8. = x5 x3 x4y7 9. = y5 x4y2 6x4y6z8 3x2y3z3 10. = 11. = 2 12x3y3

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

Examples Evaluate the following expressions. Solutions

Negative Exponents 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

Solutions Evaluate the following expressions. Rewrite the following expressions using positive exponents. Evaluate the following expressions. Solutions

Evaluate the following expressions. Rewrite the following expressions with positive exponents.