Exponent _ Rules _ Math

Exponent Rules a ×a = a m n m +n m a m −n =a n a a =1 (a ) m n =a mn a −m = m a a negative exponent "means" take the reciprocal of the base Exponent Rules x ×x x +2 x Exponent Rules ( −2 x y ) ( xy ) ( −2 ) ( 3) ( x x ) ( y 7 −6x y y ) Simplify each algebraic expression Do NOT leave negative exponents 14m −7 m 2g7gm m m m −2 = −1g7gm m m m m m m m m m Exponent Rules ( −3x y ) ( −3 x y ) ( −3 x y ) ( −3 x y ) ( −3 x y ) 5 20 81x y 12 5 Simplify the given expression Do not leave negative exponents −2 25 Simplify the given expression Do not leave negative exponents  Clear outside exponents first,  move the “location” of the base that has a negative exponent  the base still has an exponent, but now it is positive Simplify the given expression Do not leave negative exponents y y     y y  −1 −2  y y   −1  y y  2 10 y y −2 y y 14 y 12 =y y Simplify the given expression Do not leave negative exponents Clear outside exponents first, make sure all parenthesis are “gone” before “moving” bases  The base is only what the exponent touches Simplify the given expression Do not leave negative exponents x y −3 x y x yy x x y x 4 y x Simplify each numerical expression a −m = am Negative exponent, take the reciprocal of the base am = m a Rational exponent, rewrite as radical, the denominator is the index n am = m n a Rational exponent, rewrite as radical, the denominator is the index, the numerator is still the exponent of the base Simplify each numerical expression 25  1 − ÷  2 25  1  ÷  2 25 Simplify each algebraic expression Do NOT leave negative exponents   When working with rational exponents, the denominator of the exponent is the index of the radical, and the numerator is still the exponent of the base The base is only what the exponent “touches” Simplify each algebraic expression Do NOT leave negative exponents  a a 1   ÷  a 6   3 − ÷  4 2  ÷ 3 12  ÷ ÷ ÷  a ( −9 ) a a ( 2) ( 8) a Simplify each algebraic expression Do NOT leave negative exponents If n is a positive integer and m is any integer and is a real number, then m an ( = a1 / n am n ) =( ) m In radical notation: m an = ( a) n m n = a m Simplify each algebraic expression Do NOT leave negative exponents 1 −6  ÷ x y     −6 ÷ x y   1 12  − ÷ x y    −9 ÷  z   x y −3  x −2 y −4   −3 ÷ ÷  x y  z  ⇒ x y −7 x −3 y1 z x3 y8 z .. .Exponent Rules x ×x x +2 x Exponent Rules ( −2 x y ) ( xy ) ( −2 ) ( 3) ( x x ) ( y 7 −6x y y ) Simplify each algebraic expression Do NOT leave negative exponents 14m −7 m... expression Do not leave negative exponents  Clear outside exponents first,  move the “location” of the base that has a negative exponent  the base still has an exponent, but now it is positive... expression Do NOT leave negative exponents   When working with rational exponents, the denominator of the exponent is the index of the radical, and the numerator is still the exponent of the base The