# Laws of Exponent

Base Number: The number that multiplies by itself as many times as the exponent tells it to. Exponent: The small number that tells the base number how many times to multiply by itself. NOTE: numbers and variables without exponents actually have an invisible 1 as their exponent.

| | | |Multiplying exponents |EX. 22 ( 23 | |with the same base number |long way | | |2(2 ( 2(2(2 = 25 = 32 | |1.) Keep the base number. | | | |short way | |2.) Add the exponents. |22 ( 23 = 22+3 = 25 = 32 | | | | |Multiplying exponents |EX. 4x3 ( -2x4 | |with variables |long way | | |4(x(x(x ( -2(x(x(x(x= -8x7 | |1.) Multiply the base numbers. | | | |short way | |2.) Add the exponents. |4x3 ( -2x4 = -8x3+4 = -8x7 | | | | |Raising a power to a power |EX. (32 xy4 )3 | | | | |1.) Multiply the exponent |long way | |on the outside of the ( ) |(32 xy4 ) (32 xy4 ) (32 xy4 ) | |by each exponent on the | | |inside. |(3(3(x(y(y(y(y) (3(3(x(y(y(y(y) (3(3(x(y(y(y(y) | | | | |2.) Simplify the base number. |36 x3 y12 = 729 x3 y12 | | |short way...

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