Module 7 · Exponents · Lesson 30 of 39

Product and quotient rules

Multiplying same bases adds exponents; dividing subtracts them.

In this lesson · about 12 minutes

  • Use the product rule
  • Use the quotient rule
  • Know when the rules don't apply

Product rule: xa · xb = xa+b. For example x4 · x5 = x9, because that's 4 x's times 5 more x's.

Quotient rule: xaxb = xa−b. x4x3 = x1 = x: three x's on top cancel with three on the bottom.

The bases must be the same. y5x2 can't be simplified. And adding is different from multiplying: x2 + x2 + x2 − x2 = 2x2 (combining like terms), not x8.

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