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Exponent Laws

Summary of the exponent laws:

Other rules and notes

  • REMEMBER THAT ONLY PARTS/CHUNKS THAT ARE MULTIPLIED OR DIVIDED CAN BE CANCELLED.
  • Things that are in brackets are considered chunks. If there is an identical chuck then the two can be manipulated (cancelled).

· If there are addition or subtraction between terms, then one will need to remove those by FACTORING. Remember terms that are added or subtracted are not covered by the exponent laws.

· If we can find a number so that the bases are the same, then the exponents must also be the same

· If the value of two numbers is the same, and we know one base, we know the 2 nd by default, because they must be the same

· Use a trial and error approach to solve for unknown exponents and/or bases

 

Simplifying Powers

(3a 2 b)(-2a 3 b 2) = 3 × (-2) × a 2 × a 3 × b × b 2 = -6 a 2 + 3 b 1 + 2 = -6a 5 b 3

Only variables which are the same can be used together. When two variables are being multiplied we ADD their exponents.

Power of a quotient

· Reduce the quotient before you bring in the exponent.

o Same as adding exponents, but if they are in the denominator they are subtracted.

o

· When an exponent is to an exponent, we multiply the numbers together

 

Negative Exponents

· We can clear negative exponents by taking the reciprocal

o If it is a quotient, you can subtract the negative (hence making it positive)

 

Special Cases

An exponent of Zero = 1, 0 0 is not defined, there is an understood exponent of 1 if no other number appears.

 

 

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