1. Unit 5: Parts of a Power 4x 3 is an example of a monomial. The 4 is called the coefficient. The x is called the base. The 3 is called the exponent. 4x 3 = 4*x*x*x COEFFICIENTS: number being multiplied in the product BASE: the variable or number being raised to a power EXPONENT: number of the power

2. Example 1 Products of Powers Simplify each expression Product of Powers: [b](2r 4 )(-12r 7 ) [c](4ab 6 )(-7a 2 b 3 )[d](6cd 5 )(5c 5 d 2 ) PRODUCT OF POWERS: To MULTIPLY two powers that have the SAME BASES, ADD the EXPONENTS. (Coefficients get multiplied) [e] The length of a rectangle is 4xy 2 and the width is 2x 3 y 2. What is the area of the rectangle? [a](5x 7 )(x 6 )

3. Example 2 Power of a Product Simplify each expression Power of a Product: [b](3x 3 y 5 ) 3 POWER OF A POWER: Sometimes you raise an exponent to another exponent. When this happens you MULTIPLY the exponents. (Coefficients get an exponent) [c] Find the area of a square with side length 2s 2 t 4. [a](6x 2 y 3 ) 2

4. Quotient of Powers: Example 3 Quotient of Powers Simplify each expression [b] 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) [a]

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

6. 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 5 Negative Exponents Simplify each expression [b] [a]

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

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