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Exponents and Roots
Lesson 6
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Lesson 6: Exponent Laws

Use product and quotient rules for powers.

Exponent rules compress repeated multiplication into fast symbolic steps. Keep bases identical before combining exponents.

Key formula

am⋅an=am+n,  aman=am−na^m\cdot a^n=a^{m+n},\;\frac{a^m}{a^n}=a^{m-n}

Worked example

65⋅63=68=16796166^{5}\cdot 6^{3}=6^{8}=1679616

Checkpoint

In 35⋅31, what is the exponent on 3?\text{In }3^{5}\cdot 3^{1}\text{, what is the exponent on }3?

Recap

  • - Add exponents for multiplication of same base.
  • - Subtract exponents for division of same base.
  • - Use roots as fractional exponents.
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