10.5 Integer exponents and scientific notation  (Page 2/7)

When there is a product and an exponent we have to be careful to apply the exponent to the correct quantity. According to the order of operations , expressions in parentheses are simplified before exponents are applied. We’ll see how this works in the next example.

Now that we have defined negative exponents, the Quotient Property of Exponents needs only one form, $\frac{a^m}{a^n}=a^{m-n},$ where $a\ne 0$ and m and n are integers.

When the exponent in the denominator is larger than the exponent in the numerator, the exponent of the quotient will be negative. If the result gives us a negative exponent, we will rewrite it by using the definition of negative exponents, $a^{-n}=\frac{1}{a^n}.$

Simplify expressions with integer exponents

All the exponent properties we developed earlier in this chapter with whole number exponents apply to integer exponents, too. We restate them here for reference.

In the next two examples, we’ll start by using the Commutative Property to group the same variables together. This makes it easier to identify the like bases before using the Product Property of Exponents .

If the monomials have numerical coefficients, we multiply the coefficients, just as we did in Integer Exponents and Scientific Notation .