Exponent law

Exponent law

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  • If an exponential number is raised to a second exponent, the expression is simplified by multiplying the exponents.
  • Power to a power rule (Xa)b=Xab
  • (32)4 =(32)x(32)x(32)x(32) =(3x3)x(3x3)x(3x3)x(3x3) =38
  • This is the example of power to a power  
  • Power of a quotient (a)n     ----= an     (b)  ---               bn
  • The quantity of a quotient raised to a power n is the same as the quotient of each base raised to the same power of n.
  • (3)6     ----= 36     (6)6  ---               66
  • This is the example of the power  of a quotient.
  • The exponent "product rule" tells us that, when multiplying two powers that have the same base, you can add the exponents. In this example, you can see how it works. Adding the exponents is just a short cut! The "power rule" tells us that to raise a power to apower, just multiply the exponents.
  • Power of a product (ab)m=ambm
  • (2x4)5 means  (2x4)x(2x4)x(2x4)x(2x4)x(2x4) 25x46
  • This  is the example of the power of a quotient.
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