Chapter 7.2, Problem 6P

a.

To determine

To Simplify: The expression $2c^{\frac{3}{5}}\cdot 2c^{\frac{1}{5}}$

Answer to Problem 6P

The required answer is $4c^{\frac{4}{5}}$ .

Explanation of Solution

Given information:

The expression $2c^{\frac{3}{5}}\cdot 2c^{\frac{1}{5}}$

Calculation:

  $\begin{array}{l}2c^{\frac{3}{5}}\cdot 2c^{\frac{1}{5}}\\ =\left(2\cdot 2\right)\left(c^{\frac{3}{5}}\cdot c^{\frac{1}{5}}\right)\end{array}$

(Commutative and associative properties of multiplication)

  $=4\left(c^{\frac{3}{5}+\frac{1}{5}}\right)$

(Simplify. Add the exponents that have the same base)

  $=4c^{\frac{4}{5}}$

(Simplify)

b.

To determine

To Simplify: The expression $n^{\frac{1}{3}}\cdot n^{\frac{4}{3}}$ .

Answer to Problem 6P

The required answer is $n^{\frac{5}{3}}$ .

Explanation of Solution

Given information:

The expression $n^{\frac{1}{3}}\cdot n^{\frac{4}{3}}$

Calculation:

  $\begin{array}{l}{n}^{\frac{1}{3}}\cdot n^{\frac{4}{3}}\\ =n^{\frac{1}{3}+\frac{4}{3}}\end{array}$

(Add the exponents that have the same base)

  $=n^{\frac{5}{3}}$

(Simplify)

c.

To determine

To Simplify: The expression $\left(b^{\frac{2}{3}}\cdot c^{\frac{2}{5}}\right)\left(b^{\frac{4}{9}}\cdot c^{\frac{9}{10}}\right)$

Answer to Problem 6P

The required answer is $b^{\frac{10}{9}}{c}^{\frac{13}{10}}$ .

Explanation of Solution

Given information:

The expression $\left(b^{\frac{2}{3}}\cdot c^{\frac{2}{5}}\right)\left(b^{\frac{4}{9}}\cdot c^{\frac{9}{10}}\right)$

Calculation:

  $\begin{array}{l}\left(b^{\frac{2}{3}}\cdot c^{\frac{2}{5}}\right)\left(b^{\frac{4}{9}}\cdot c^{\frac{9}{10}}\right)\\ =\left(b^{\frac{2}{3}}\cdot b^{\frac{4}{9}}\right)\left(c^{\frac{2}{5}}\cdot c^{\frac{9}{10}}\right)\end{array}$

(Commutative and associative properties of multiplication)

  $=b^{\frac{10}{9}}{c}^{\frac{13}{10}}$

(Add the exponents that have the same base)

d.

To determine

To Simplify: The expression $\left(3j^{\frac{2}{3}}\cdot 7m^{\frac{1}{4}}\right)\left(3j^{\frac{1}{6}}\cdot 7m^{\frac{3}{2}}\right)$ .

Answer to Problem 6P

The required answer is

Explanation of Solution

Given information:

The expression $\left(3j^{\frac{2}{3}}\cdot 7m^{\frac{1}{4}}\right)\left(3j^{\frac{1}{6}}\cdot 7m^{\frac{3}{2}}\right)$

Calculation:

  $\begin{array}{l}\left(3j^{\frac{2}{3}}\cdot 7m^{\frac{1}{4}}\right)\left(3j^{\frac{1}{6}}\cdot 7m^{\frac{3}{2}}\right)\\ =\left(3\cdot 7\cdot 3\cdot 7\right)\left(j^{\frac{2}{3}}\cdot j^{\frac{1}{6}}\right)\left(m^{\frac{1}{4}}\cdot m^{\frac{3}{2}}\right)\end{array}$

(Commutative and associative properties of multiplication)

  $=441\left(j^{\frac{2}{3}}\cdot j^{\frac{1}{6}}\right)\left(m^{\frac{1}{4}}\cdot m^{\frac{3}{2}}\right)$

(Simplify)

  $=441j^{\frac{5}{6}}{m}^{\frac{7}{4}}$

(Add the exponents that have the same base)