The Seven Rules of Indices:
Rule 1: When multiplying powers of the same base, add the two powers together.
Example: a^m x a^n = a^(m+n) Rule 2: When dividing powers of the same base, subtract the second power from the first. Example: a^m / a^n = a^(m-n) Rule 3: When multiplying a power by a power outside of a pair of brackets, multiply the two powers together. Example: (a^m)^n = a^(mn) Rule 4: When multiplying a base by a negative power, divide one by the base raised to the positive power. Example: a^-m = 1/a^m |
Rule 5: When multiplying a base by a fractional power, square root the base to the degree of the denominator and raise the base by the power of the numerator. (The order in which you solve this does not matter, you can root the base then raise to the power, or you can raise the base to the power, then root the answer)
Example: a^(m/n) = n√(a^m) Rule 6: When raising a base by the power of 1, the answer always equal the base. Example: a¹ = a Rule 7: When raising a base by the power of 0, the answer always equals 1. Example: a^0 = 1 |