And Scientific Notation

Power Property (ax m ) n = (a n )x m·n Coefficient: Raise to outside exponent Base: same Exponent: Multiply inside by outside (5x 6 ) 3 = (5 3 )x 6·3 = 125x 18

Zero and Negative Exponents Anything raised to the zero power equals one. Negative exponents flip fractions 1) Move exponent and base to opposite side of the fraction 2) Change exponent from neg to pos Negative exponents move; Zero exponents disappear; Positive exponents stay

Product Property (ax m )(bx n ) = (ab)x m+n Coefficient: Multiply Base: same Exponent: Add (2x 5 )(4x 6 ) = (2·4)x 5+6 = 8x 11

Quotient Property Coefficient: Divide or reduce if possible Base: same Exponent: subtract (do you have more on top or bottom?)

Miscellaneous Items Suggested order: order of operations Parentheses (Power Property) coeff: raise to outside exponentexponents: multiply inside by outside Exponents(Zero and Negative Exponents) neg exponents move; zero exponents disappear; pos exponents stay Multiply(Product Property) coeff: multiplyexponents: add Divide(Quotient Property) coeff: divideexponents: subtract Exponents outside go with everything inside … both top and bottom

Scientific Notation C x 10 n Coefficient is always between 1 and 10 Can equal one but cannot equal 10 1 ≤ C < 10 Base is always 10 Exponent can be any integer (positive or negative; no fractions or decimals) Positive exponents Large numbers Negative exponentsSmall numbers Indicates number of places to move decimal 5.23 x = x =

Operations with Scientific Notation Power Property(a x 10 m ) n = a n x 10 mn Coefficient: raise to outside exponent Base: stays the same (10) Exponents: multiply inside exponent by outside exponent Product Property(a x 10 m )(b x 10 n ) = (ab) x 10 m+n Coefficient: multiply Base: stays the same (10) Exponents: add Quotient Property a x 10 m = a x 10 m-n b x 10 n b Coefficient: divide (decimal answer) Base: stays the same (10) Exponents: subtract top minus bottom (negative exponents ok)

Adding and Subtracting Scientific Notation Numbers Need “like terms”: same base (10) and same exponent Always change the smaller exponent to the larger Recall that while 2 is less than 4; -4 is less than -2 The number added to the exponent indicates how many places the decimal gets moved in the coefficient (always move to the left) Once you have both numbers with the same exponent Add or subtract the coefficients as indicated Base and exponent stays the same

Examples: (3.24 x 10 4 ) + (6.05 x 10 6 ) = ( x ) + (6.05 x 10 6 ) = ( ) + (6.05 x 10 6 ) = ( ) x 10 6 = x 10 6 (5.1 x ) - (7.4 x ) = (5.1 x ) - (0.74 x ) = ( ) - (0.74 x ) = ( ) x = 4.36 x 10 -3