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Exercises Polynomials and factoring

Example 10.47 from Prealgebra, 10.4 Divide Monomials

Divide Monomials: example 10.47

Simplify:

ⓐ $\frac{a^{5}}{a^{9}}$
ⓑ $\frac{x^{11}}{x^{7}}$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution

ⓐ

Since 9 > 5, there are more $a$ 's in the denominator and so we will end up with factors in the denominator. $\frac{a^{5}}{a^{9}}$

Use the Quotient Property for $n > m, \frac{a^{m}}{a^{n}} = \frac{1}{a^{n - m}} .$

Simplify. $\frac{1}{a^{4}}$

ⓑ

Notice there are more factors of $x$ in the numerator, since 11 > 7. So we will end up with factors in the numerator. $\frac{x^{11}}{x^{7}}$

Use the Quotient Property for $m > n, \frac{a^{m}}{a^{n}} = a^{n - m} .$

Simplify. $x^{4}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Simplify:

ⓐ $\frac{b^{19}}{b^{11}}$
ⓑ $\frac{z^{5}}{z^{11}}$

How did it go?

PreviousDivide Monomials: example 10.46 Next Divide Monomials: example 10.48

From Prealgebra (1st edition) by OpenStax (Rice University), section 10.4, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.