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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 9: Q574. (page 1144)

Use the Laws of Exponents to Simplify Expressions with Rational Exponents
$(a) \frac{x^{\frac{7}{2}}}{x^{\frac{5}{2}}} (b) \frac{y^{\frac{5}{2}}}{y^{\frac{1}{2}}} (c) \frac{r^{\frac{4}{5}}}{r^{\frac{9}{5}}} .$

Short Answer

Expert verified

Part (a) $\frac{x^{\frac{7}{2}}}{x^{\frac{5}{2}}} = x$

Part (b) $\frac{y^{\frac{5}{2}}}{y^{\frac{1}{2}}} = y^{2}$

Part (c) $\frac{r^{\frac{4}{5}}}{r^{\frac{9}{5}}} = \frac{1}{r}$

Step by step solution

01

Part (a)Step 1:Given information

The given expression is $\frac{x^{\frac{7}{2}}}{x^{\frac{5}{2}}} .$

02

Part (a)Step 2:Simplification

To raise a power to a power, we multiply the exponents.

$\frac{x^{\frac{7}{2}}}{x^{\frac{5}{2}}} = x^{\frac{7}{2} - \frac{5}{2}} = x^{\frac{7 - 5}{2}} = x H e n c e, \frac{x^{\frac{7}{2}}}{x^{\frac{5}{2}}} = x .$

03

Part (b)Step 1:Given information

The given expression is $\frac{y^{\frac{5}{2}}}{y^{\frac{1}{2}}} .$

04

Part (b)Step 2:Simplification

To raise a power to a power, we multiply the exponents.

$\frac{y^{\frac{5}{2}}}{y^{\frac{1}{2}}} = y^{\frac{5}{2} - \frac{1}{2}} = y^{2} H e n c e, \frac{y^{\frac{5}{2}}}{y^{\frac{1}{2}}} = y^{2} .$

05

Part (c)Step 1:Given information

The given expression is $\frac{r^{\frac{4}{5}}}{r^{\frac{9}{5}}} .$

06

Part (c) Step 2:Simplification

To raise a power to a power, we multiply the exponents.
$\frac{r^{\frac{4}{5}}}{r^{\frac{9}{5}}} = r^{\frac{4 - 9}{5}} = r^{- 1} = \frac{1}{r} H e n c e, \frac{r^{\frac{4}{5}}}{r^{\frac{9}{5}}} = \frac{1}{r} .$

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Most popular questions from this chapter

Try It.

Sergio wants to make a square mosaic as an inlay for a table he is building. He has enough tile to cover an area of $2704$ square centimeters. Use the formula $s = \sqrt{A}$ to find the length of each side of his mosaic. Round your answer to the nearest tenth of a centimeter.

Try It.

Katie wants to plant a square lawn in her front yard. She has enough sod to cover an area of $370$ square feet. Use the formula $s = \sqrt{A}$ to find the length of each side of her lawn. Round your answer to the nearest tenth of a foot.

Accident investigation: The skid marks for a car involved in an accident measured 216 feet. Use the formula $s = \sqrt{24 d}$ to find the speed of the car before the brakes were applied. Round your answer to the nearest tenth.

In the following exercises, simplify and rationalize the denominator.

$- \frac{8}{3 \sqrt{6}}$

In the following exercises, solve.

$\sqrt{5 q + 3} - 4 = 0$ .

See all solutions

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