Chapter ISG, Problem 7.3.2P

a.

To determine

To find an equivalent expression

Answer to Problem 7.3.2P

  $w^{\frac{13}{2}}{x}^{\frac{5}{2}}{z}^{\frac{9}{2}}$ is the equivalent expression.

Explanation of Solution

Given information:

  $\sqrt{w^{13}{x}^5{z}^8}$

Calculation:

The given equation is $\sqrt{w^{13}{x}^5{z}^8}$

Rooting both sides,

= $\sqrt{w^{2(6)+1}{x}^{2(2)+1}{z}^{2(4)}}$

So,

= $w^6{x}^2{z}^4\sqrt{wxz}$

Rearranging,

= $w^{6+\frac{1}{2}}{x}^{2+\frac{1}{2}}{z}^{4+\frac{1}{2}}$

Solving,

= $w^{\frac{13}{2}}{x}^{\frac{5}{2}}{z}^{\frac{9}{2}}$

Hence, $w^{\frac{13}{2}}{x}^{\frac{5}{2}}{z}^{\frac{9}{2}}$ is the equivalent expression.

b.

To determine

To find an equivalent expression

Answer to Problem 7.3.2P

  $2m^8$ is the equivalent expression.

Explanation of Solution

Given information:

  $\sqrt[4]{16m^{32}}$

Calculation:

The given equation is $\sqrt[4]{16m^{32}}$

Rooting the equation,

= $\sqrt[4]{{(2)}^4{m}^{4(8)}}$

So,

= $2m^8$

Hence, $2m^8$ is the equivalent expression.

c.

To determine

To find an equivalent expression

Answer to Problem 7.3.2P

  $x^{\frac{5}{6}}$ is the expression

Explanation of Solution

Given information:

  $(\sqrt{x})(\sqrt[3]{x})$

Calculation:

The given expression $(\sqrt{x})(\sqrt[3]{x})$

The equation can be written as

= $x^{\frac{1}{2}}{x}^{\frac{1}{3}}$

Using law of exponent $a^m.a^n=a^{m+n}$

= $x^{\frac{1}{3}+\frac{1}{2}}$

So,

= $x^{\frac{3+2}{6}}$

Hence,

  $x^{\frac{5}{6}}$ is the expression

d.

To determine

To find an equivalent expression

Answer to Problem 7.3.2P

  $b^{\frac{1}{6}}$ is the equivalent expression.

Explanation of Solution

Given:

  $\sqrt[3]{\sqrt{b}}$

Calculation:

The given equation is $\sqrt[3]{\sqrt{b}}$

The expression can be written as,

= $\sqrt[3]{b^{\frac{1}{2}}}$

Rearranging the expression,

= $b^{\frac{\frac{1}{2}}{3}}$

So,

= $b^{\frac{1}{2\times 3}}$

Hence, $b^{\frac{1}{6}}$ is the equivalent expression.