Skip to content

Physics Playground

Simulations How we teach Pricing

Language

Log in Start learning free

Loading…

Physics Playground

Built on open, peer-reviewed sources: OpenStax, The Feynman Lectures on Physics, HyperPhysics, NASA and NIST. See our sources.

Learn

Physics course
Math for Physics
Start with the math toolkit
Simulations
Glossary
Exercises
Past exams
Library
How we teach

Company

Pricing
Terms
Privacy
Contact

© 2026 Physics Playground. Made for the curious.Language

Exercises Polynomials and factoring

Example 10.46 from Prealgebra, 10.4 Divide Monomials

Divide Monomials: example 10.46

Simplify:

ⓐ $\frac{b^{10}}{b^{15}}$
ⓑ $\frac{3^{3}}{3^{5}}$

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
To simplify an expression with a quotient, we need to first compare the exponents in the numerator and denominator.

ⓐ

Since 15 > 10, there are more factors of $b$ in the denominator. $\frac{b^{10}}{b^{15}}$

Use the quotient property with $n > m, \frac{a^{m}}{a^{n}} = \frac{1}{a^{n - m}} .$

Simplify. $\frac{1}{b^{5}}$

ⓑ

Since 5 > 3, there are more factors of 3 in the denominator. $\frac{3^{3}}{3^{5}}$

Use the quotient property with $n > m, \frac{a^{m}}{a^{n}} = \frac{1}{a^{n - m}} .$

Simplify. $\frac{1}{3^{2}}$

Apply the exponent. $\frac{1}{9}$

Notice that when the larger exponent is in the denominator, we are left with factors in the denominator and $1$ in the numerator.

Your turn

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

Simplify:

ⓐ $\frac{x^{8}}{x^{15}}$
ⓑ $\frac{12^{11}}{12^{21}}$

How did it go?

PreviousDivide Monomials: example 10.45 Next Divide Monomials: example 10.47

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.