Chapter 7.2, Problem 4P

a.

To determine

To Simplify: The expression ${16}^{\frac{1}{4}}$ .

Answer to Problem 4P

The required answer is 2.

Explanation of Solution

Given information:

The expression ${16}^{\frac{1}{4}}$

Calculation:

  $\begin{array}{l}{16}^{\frac{1}{4}}\\ ={\left(2\cdot 2\cdot 2\cdot 2\right)}^{\frac{1}{4}}\end{array}$

(Find the number that when multiplied by itself four times gives 16)

  $\begin{array}{l}={\left(2^4\right)}^{\frac{1}{4}}\\ =2\end{array}$

(Simplify)

b.

To determine

To Simplify: The expression ${27}^{\frac{1}{3}}$ .

Answer to Problem 4P

The required answer is3.

Explanation of Solution

Given information:

The expression ${27}^{\frac{1}{3}}$

Calculation:

  $\begin{array}{l}{27}^{\frac{1}{3}}\\ ={\left(3\cdot 3\cdot 3\right)}^{\frac{1}{3}}\end{array}$

(Find the number that when multiplied by itself three times gives 27)

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

(Simplify)

c.

To determine

To Simplify: The expression ${64}^{\frac{1}{2}}$ .

Answer to Problem 4P

The required answer is 8

Explanation of Solution

Given information:

  ${64}^{\frac{1}{2}}$

Calculation:

  $\begin{array}{l}{64}^{\frac{1}{2}}\\ ={\left(8\cdot 8\right)}^{\frac{1}{2}}\end{array}$

(Find the number that when multiplied by itself two times gives 64)

  $\begin{array}{l}={\left(8^2\right)}^{\frac{1}{2}}\\ =8\end{array}$

(Simplify)