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WHEN MULTIPLYING LIKE BASES, YOU ADD THE EXPONENTS a a a n m n m FOR EXAMPLE: 3 3 3 2 5 2 5 3 7 NOW YOU TRY: 4 4 4 6 4 6 4 4 10 WHEN RAISING A POWER TO A POWER, YOU MULTIPLY THE EXPONENTS a n m a nm FOR EXAMPLE: 3 4 6 3 4 *6 3 24 NOW YOU TRY: 4 3 5 4 3*5 41 5 ANY INTEGER RAISED TO NEGATIVE ONE IS THE RECIPROCAL OF THAT INTEGER. a 1 1 a FOR EXAMPLE: 3 1 1 3 NOW YOU TRY: 15 1 1 15 Any fraction raised to negative one is the reciprocal of that fraction. a b 1 b a FOR EXAMPLE: 2 5 1 5 2 NOW YOU TRY: 9 15 1 15 9 WHEN DIVIDING LIKE BASES, YOU SUBTRACT THE EXPONENTS. an am n m a FOR EXAMPLE: x5 x3 x 5 3 x 2 NOW YOU TRY: x 12 12 4 8 x x x4 ANY NUMBER RAISED TO THE FIRST POWER IS ITSELF. a a 1 FOR EXAMPLE: 3 3 1 NOW YOU TRY: 528921 528921 1 ANY NUMBER RAISED TO THE ZERO POWER IS ONE. a 1 0 FOR EXAMPLE: 3 1 0 NOW YOU TRY: 528921 1 0 HOW DO WE GET ANY NUMBER RAISED TO THE ZERO POWER EQUAL TO ONE? 0 a 0 a 1 Can be written as a 11 Working backward-you subtract the exponents when you are dividing like bases. a 11 a1 a1 Then any number divided by itself will give you ONE!!! TRY THESE ON YOUR OWN: x 3 x 5 x 3 x 5 1 1 2 x 4 1 8 x TRY THESE ON YOUR OWN: x 4 y 1 3 4 x y x 4 y x y 3 3 3 4 TRY THIS LAST ONE ON YOUR OWN: a b a 5 7 9 a b b 3 2 8