Not so EXTRATERRESTRIAL

For each of the following, can you identify the base and the exponent?     If a number doesn’t have an exponent, then you can always assume the exponent is 1  Ex: 7=7 1

Vocab  Polynomial-  Monomial-  Constant-  Coefficient-  Zero exponent-  Negative exponent-

Polynomial  An algebraic expression consisting of variables, coefficients, and constants, involving only the operations of addition, subtraction, multiplication and non negative whole exponents  Examples:  6x+4  15h-17h 2  m 3 +2m 2 +4

Monomial-  A single algebraic term  May be….  A constant  A variable  A product of a constant and a variable

Laws of Exponents  Product (multiplication) of Powers (a m )(a n ) = a m+n  Multiply the coefficients, ADD the exponents! Example 1:x 5 x 2 =

ADD the exponents!  Example 2:x 3 y -2 =  Example 3:(5x 4 y 8 )(3x -3 y) =

Practice!  1) k 4 k -2 k 3 =  2) h 7 g -1 h 5 =  3) (2a 3 b 4 c -5 )(4ab -8 ) =

TIC TAC TOE!

Laws of Exponents  Power of a Power (a m ) n = a mn MULTIPLY the exponents!  Example 1:(x 5 ) -2 =

More Examples!  Example 2:(x 3 ) 3 =  Example 3:(y 8 ) -4 =

Practice!  1) (k 4 ) 8 =  2) (g -1 ) 5 =  3) (c -5 ) -2 =

Power of Power with more than one number, variable, etc  (4x) 2 requires that you distribute the 2 to the 4 and the x  4 2 x 2

Try these!  (gm) 6  (4w 3 ) 3

Sometimes you have to use both…  What if you have (2v) 2 (2v)  First distribute the power outside the parentheses to the info inside  Then use what we learned about adding exponents and multiplying coefficients

Try this…(ba 4 )(2ba 4 ) 3

Dividing Exponents 

More examples 

Negative Exponents  Bottom line: We don’t like em!  So how do we get rid of em?  Move them

Any number except 0 with a negative exponent equals its reciprocal with the opposite exponent. Negative Exponents

Evaluating Negative Exponents  Write the reciprocal, change the sign of the exponent  Simplify