Rules of Exponents: product, quotient, power rules

Rules of Exponents

1. Product Rule

   • A^m . A^n = A^m+n
     • Ex. x^5 . x^2 = x^7

2. Quotient Rule

   • A^m / A^n = A^m-n
     • Ex. x^7 / x^2 = x^5

3. Negative Exponent Rule

   • A^-m = 1 / A^m
     • Ex. x^-2 = 1 / x^2

4. Zero Exponent Rule

   • A^0 = 1
     • Ex. 2^0 = 1

5. Raising a Power to a Power

   • (A^m)n = A^mn
     • Ex. (x^2)3 = x^6

6. Raising a Product to a Power

   • (AB)m = A^m B^n
     • Ex. (xy)2 = x^2 y^2

7. Raising a Quotient to a Power

   • (A/B)m = A^m / B^m
     • Ex. (x/y)2 = x^2 / y^2

8. Product Rule for Radicals