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 10.67 from Prealgebra, 10.5 Integer Exponents and Scientific Notation

Integer Exponents and Scientific Notation: example 10.67

Simplify:

ⓐ $5 y^{−1}$
ⓑ ${(5 y)}^{−1}$
ⓒ ${(−5 y)}^{−1}$

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

ⓐ

Notice the exponent applies to just the base $5 y$ . $5 y^{−1}$

Take the reciprocal of $y$ and change the sign of the exponent. $5 \cdot \frac{1}{y^{1}}$

Simplify. $\frac{5}{y}$

ⓑ

Here the parentheses make the exponent apply to the base $5 y$ . ${(5 y)}^{−1}$

Take the reciprocal of $5 y$ and change the sign of the exponent. $\frac{1}{{(5 y)}^{1}}$

Simplify. $\frac{1}{5 y}$

ⓒ

${(−5 y)}^{−1}$

The base is $- 5 y$ . Take the reciprocal of $- 5 y$ and change the sign of the exponent. $\frac{1}{{(−5 y)}^{1}}$

Simplify. $\frac{1}{−5 y}$

Use $\frac{a}{- b} = - \frac{a}{b} .$ $- \frac{1}{5 y}$

Your turn

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

Simplify:

ⓐ $8 p^{−1}$
ⓑ ${(8 p)}^{−1}$
ⓒ ${(−8 p)}^{−1}$

How did it go?

PreviousInteger Exponents and Scientific Notation: example 10.66 Next Integer Exponents and Scientific Notation: example 10.68

From Prealgebra (1st edition) by OpenStax (Rice University), section 10.5, 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.