Chapter 8: Q. 151 (page 787)

In the following exercises, simplify.
(a) $c^{\frac{1}{4}} \cdot c^{\frac{5}{8}}$
(b) ${(p^{12})}^{\frac{3}{4}}$
(c) $\frac{r^{\frac{4}{5}}}{r^{\frac{9}{5}}}$

Short Answer

Expert verified

(a) The answer is $c^{\frac{7}{8}}$

(b) The answer is $p^{9}$

Step by step solution

Step 1. Part (a) Simplify the expression c14·c58

We will use the property

$a^{m} \cdot a^{n} = a^{m + n}$

$c^{\frac{1}{4}} \cdot c^{\frac{5}{8}} = c^{\frac{1}{4} + \frac{5}{8}} = c^{\frac{2 + 5}{8}} = c^{\frac{7}{8}}$

Step 2. Part (b) Simplify the expression p1234

We will use the property

${(a^{m})}^{n} = a^{m n}$

${(p^{12})}^{\frac{3}{4}} = p^{12 \times \frac{3}{4}} = p^{9}$

Step 3. Part (c) Simplify the expressionr45r95

We will use the property

$\frac{a^{m}}{a^{n}} = a^{m - n}$

$\frac{r^{\frac{4}{5}}}{r^{\frac{9}{5}}} = r^{\frac{4}{5} - \frac{9}{5}} = r^{- 1} = \frac{1}{r}$

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In the following exercises, simplify.
(a) $c^{\frac{1}{4}} \cdot c^{\frac{5}{8}}$
(b) ${(p^{12})}^{\frac{3}{4}}$
(c) $\frac{r^{\frac{4}{5}}}{r^{\frac{9}{5}}}$

Short Answer

Step by step solution

Step 1. Part (a) Simplify the expression c14·c58

Step 2. Part (b) Simplify the expression p1234

Step 3. Part (c) Simplify the expressionr45r95

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In the following exercises, simplify.(a) c14·c58(b) p1234(c)r45r95

Short Answer

Step by step solution

Step 1. Part (a) Simplify the expression c14·c58

Step 2. Part (b) Simplify the expression p1234

Step 3. Part (c) Simplify the expressionr45r95

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Probability and Statistics

Logic and Functions

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify.
(a) $c^{\frac{1}{4}} \cdot c^{\frac{5}{8}}$
(b) ${(p^{12})}^{\frac{3}{4}}$
(c) $\frac{r^{\frac{4}{5}}}{r^{\frac{9}{5}}}$