Unit 5: Parts of a Power

1. Unit 5: Parts of a Power

2. Product of Powers: PRODUCT OF POWERS: To MULTIPLY two powers that have the SAME BASES, ADD the EXPONENTS. (Coefficients get multiplied) Example 1Products of Powers Simplify each expression [a] (5x7)(x6) [b] (2r4)(-12r7) [c] (4ab6)(-7a2b3) [d] (6cd5)(5c5d2) [e] The length of a rectangle is 4xy2and the width is 2x3y2. What is the area of the rectangle?

3. Power of a Product: POWER OF A POWER: Sometimes you raise an exponent to another exponent. When this happens you MULTIPLY the exponents. (Coefficients get an exponent) Example 2Power of a Product Simplify each expression [b] (3x3y5)3 [a] (6x2y3)2 [c] Find the area of a square with side length 2s2t4.

4. [a] [b] Quotient of Powers: When you DIVIDE monomials of LIKE BASES, you SUBTRACT Big Minus Small Exponent. Put the answer in the location of the big exponent (top or bottom). (Coefficients get divided or reduced) Example 3Quotient of Powers Simplify each expression

5. [a] [b] Zero Exponent: ANYTHING RAISED TO THE ZERO POWER = 1!!!!!!!! (Be Careful of what it touches) Example 4Quotient of Powers Simplify each expression

6. [a] [b] Negative Exponents: Negative on top move to bottom as POSITIVE Negative on bottom move to top as POSITIVE (Be careful what the negative touches) Example 5Negative Exponents Simplify each expression

7. Fraction Exponents: Example 6 Rewrite each example in radical form. [b] [a] [c] Rewrite each example in fraction form. [e] [d] [f]

8. Distributing Fraction Exponents Example 7 Simplify completely [a] [b] [d] [c]