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Rules of exponents

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Orlando Calderon

The document discusses several rules and properties related to exponents: 1) When multiplying like bases, you add the exponents. 2) When raising a power to a power, you multiply the exponents. 3) Any integer raised to a negative one power is the reciprocal of that integer. 4) Any number raised to the first power is itself, and any number raised to the zero power is one.

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Rules of exponents
WHEN MULTIPLYING LIKE BASES, YOU ADD THE EXPONENTS ( )( ) 75252 3333 == + FOR EXAMPLE: NOW YOU TRY: ( )( ) =46 44 ( )( ) =mn aa mn a + 1046 44 =+
WHEN RAISING A POWER TO A POWER, YOU MULTIPLY THE EXPONENTS FOR EXAMPLE: NOW YOU TRY: ( ) nmmn aa = ( ) 246*464 333 == ( ) = 53 4 155*3 44 =
ANY INTEGER RAISED TO NEGATIVE ONE IS THE RECIPROCAL OF THAT INTEGER. FOR EXAMPLE: NOW YOU TRY: a a 11 =− 3 1 3 1 =− =−1 15 15 1
Any fraction raised to negative one is the reciprocal of that fraction. FOR EXAMPLE: NOW YOU TRY: a b b a =      −1 2 5 5 2 1 =      − =      −1 15 9 9 15
WHEN DIVIDING LIKE BASES, YOU SUBTRACT THE EXPONENTS. FOR EXAMPLE: NOW YOU TRY: mn m n a a a − =      235 3 5 xx x x ==      − =      4 12 x x 8412 xx =−
ANY NUMBER RAISED TO THE FIRST POWER IS ITSELF. FOR EXAMPLE: NOW YOU TRY: aa =1 331 = =1 528921 528921
ANY NUMBER RAISED TO THE ZERO POWER IS ONE. FOR EXAMPLE: NOW YOU TRY: 10 =a 130 = =0 528921 1
HOW DO WE GET ANY NUMBER RAISED TO THE ZERO POWER EQUAL TO ONE? 10 =a 0 a can be written as 11− a Working backward-you subtract the exponents when you are dividing like bases. 1 1 11 a a a =− Then any number divided by itself will give you ONE!!!
TRY THESE ON YOUR OWN: =      −1 3 5 x x =      −4 3 5 x x 2 1 x 8 1 x
TRY THESE ON YOUR OWN: = − 4 3 y x =−4 3 y x 43 1 yx 43 yx
TRY THIS LAST ONE ON YOUR OWN: =− − 75 23 ba ba 9 8 b a

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Rules of exponents

  • 2. WHEN MULTIPLYING LIKE BASES, YOU ADD THE EXPONENTS ( )( ) 75252 3333 == + FOR EXAMPLE: NOW YOU TRY: ( )( ) =46 44 ( )( ) =mn aa mn a + 1046 44 =+
  • 3. WHEN RAISING A POWER TO A POWER, YOU MULTIPLY THE EXPONENTS FOR EXAMPLE: NOW YOU TRY: ( ) nmmn aa = ( ) 246*464 333 == ( ) = 53 4 155*3 44 =
  • 4. ANY INTEGER RAISED TO NEGATIVE ONE IS THE RECIPROCAL OF THAT INTEGER. FOR EXAMPLE: NOW YOU TRY: a a 11 =− 3 1 3 1 =− =−1 15 15 1
  • 5. Any fraction raised to negative one is the reciprocal of that fraction. FOR EXAMPLE: NOW YOU TRY: a b b a =      −1 2 5 5 2 1 =      − =      −1 15 9 9 15
  • 6. WHEN DIVIDING LIKE BASES, YOU SUBTRACT THE EXPONENTS. FOR EXAMPLE: NOW YOU TRY: mn m n a a a − =      235 3 5 xx x x ==      − =      4 12 x x 8412 xx =−
  • 7. ANY NUMBER RAISED TO THE FIRST POWER IS ITSELF. FOR EXAMPLE: NOW YOU TRY: aa =1 331 = =1 528921 528921
  • 8. ANY NUMBER RAISED TO THE ZERO POWER IS ONE. FOR EXAMPLE: NOW YOU TRY: 10 =a 130 = =0 528921 1
  • 9. HOW DO WE GET ANY NUMBER RAISED TO THE ZERO POWER EQUAL TO ONE? 10 =a 0 a can be written as 11− a Working backward-you subtract the exponents when you are dividing like bases. 1 1 11 a a a =− Then any number divided by itself will give you ONE!!!
  • 10. TRY THESE ON YOUR OWN: =      −1 3 5 x x =      −4 3 5 x x 2 1 x 8 1 x
  • 11. TRY THESE ON YOUR OWN: = − 4 3 y x =−4 3 y x 43 1 yx 43 yx
  • 12. TRY THIS LAST ONE ON YOUR OWN: =− − 75 23 ba ba 9 8 b a