Rules of Exponents

Rules of Exponents

1. Product Rule

   • a^m * a^n = a^m+n
     • Example: 3a^-2 * 4a^-6 = 12a^-8

2. Rasing a Product to a Power

   • (ab)^m=a^mb^m
     • Example: (2x)^4 = 2^4 x^4 = 16x^4

3. Quotient Rule

   • a^m/a^n= a^m-n
     • Example: 5w^-2/w^-7 = 5w^5

4. Negative Exponent Rule

   • a^-m= 1/am
     • Example: 10^-9 =1/10^9

5. Product Rule for Radicals

   • n√a * n √b = n√ab
     • Example: √2 * √6 = √12 = √2^3 *3 = 2√3

6. Zero Exponent Rule

   • a^0= 1
     • Example: 5^0 = 1

7. Raising a power to a Power

   • (a^m)^n=a^m*n
     • Example: (b^-4)^-3= b^-12

8. Rasing a Quotient to a Power

   • (a/b)^m= a^m/b^m
     • Example: (1/2)^3= 1^3/2^3

9. Quotient Rule for Radicals

   • n√a/n√b = n√a/b
     • Example: 4√8/8√2 = 4/8 * √14/√2 = 1/2 *14√2 = 1/2 √7 = √7/2

10. Exponential form of n√a^n

    • If the Indez and the exponent is the same you cancel them.
      • n√a^n = (n√a)^n= a^n/n= a
        • Example: √4^2 = 4^2/2 = 4

11. Exponential form of n√a

    • -When ''a'' is a nonnegative, n can be any index. -When ''a'' is a negative, ''n'' must be odd.
      • n√a= a^1/n
        • Example: 8√4 = 4^1/n

12. Exponential form of n√a^m

    • -For every nonnegative number a, and integers m and n.
      • n√a^m = (n√a)^m = a^m/n
        • Example:3√4^11 = (3√4)^11 = 4^11/3