Laws of Exponents

Laws of Exponents

The same laws hold for rational-number exponents as for integer exponents.

We list them for review.

For any real number a and any rational exponents m and n:

a. a^m.aⁿ= a^m+n In multiplying, we can add exponents if the

bases are the same.

b. $\frac{a^{m}}{a^{n}}$ = a^m.n In dividing, we can subtract exponents if the

bases are the same.

c. (a^m)n = a^m.nTo raise a power to a power, we can multiply

the exponents.

d. (ab)^m = a^mb^m To raise a product to a power, we can raise

each factor to the power.

e. $(\frac{a}{b})^{n} = \frac{a^{n}}{b^{n}}$ To raise a quotient to a power, we can raise

both the numerator and the denominator to

the power.