Chapter 8: Q 157E (page 788)

In the following exercises, simplify:
Part (a): ${(16 u^{\frac{1}{3}})}^{\frac{3}{4}}$
Part (b): ${(4 p^{\frac{1}{3}} q^{\frac{1}{2}})}^{\frac{3}{2}}$

Short Answer

Expert verified

Part (a): On simplifying, we get $8 u^{\frac{1}{4}}$ .

Part (b): On simplifying, we get $8 p^{\frac{1}{2}} q^{\frac{3}{4}}$ .

Step by step solution

Part (a) Step 1. Given information.

Consider the given question,

${(16 u^{\frac{1}{3}})}^{\frac{3}{4}}$

First we use the product to a power property,

$= {(16)}^{\frac{3}{4}} {(u^{\frac{1}{3}})}^{\frac{3}{4}}$

Rewrite $16$ as a power of role="math" localid="1644860605785" $2$ ,

$= {(2^{4})}^{\frac{3}{4}} {(u^{\frac{1}{3}})}^{\frac{3}{4}} = (2^{4 \times \frac{3}{4}}) (u^{\frac{1}{3} \times \frac{3}{4}}) = (2^{3}) (u^{\frac{1}{4}}) = 8 u^{\frac{1}{4}}$

Part (b) Step 1. Given information.

Consider the given question,

${(4 p^{\frac{1}{3}} q^{\frac{1}{2}})}^{\frac{3}{2}}$

First we use the product to a power property,

$= {(4)}^{\frac{3}{2}} {(p^{\frac{1}{3}})}^{\frac{3}{2}} {(q^{\frac{1}{2}})}^{\frac{3}{2}}$

Rewrite $4$ as a power of $2$ ,

role="math" localid="1644860929813" $= {(2^{2})}^{\frac{3}{2}} {(p^{\frac{1}{3}})}^{\frac{3}{2}} {(q^{\frac{1}{2}})}^{\frac{3}{2}} = (2^{2 \times \frac{3}{2}}) (p^{\frac{1}{3} \times \frac{3}{2}}) (q^{\frac{1}{2} \times \frac{3}{2}}) = (2^{3}) (p^{\frac{1}{2}}) (q^{\frac{3}{4}}) = 8 p^{\frac{1}{2}} q^{\frac{3}{4}}$

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In the following exercises, simplify:
Part (a): ${(16 u^{\frac{1}{3}})}^{\frac{3}{4}}$
Part (b): ${(4 p^{\frac{1}{3}} q^{\frac{1}{2}})}^{\frac{3}{2}}$

Short Answer

Step by step solution

Part (a) Step 1. Given information.

Part (b) Step 1. Given information.

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In the following exercises, simplify:Part (a):16u1334Part (b):4p13q1232

Short Answer

Step by step solution

Part (a) Step 1. Given information.

Part (b) Step 1. Given information.

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

In the following exercises, simplify:
Part (a): ${(16 u^{\frac{1}{3}})}^{\frac{3}{4}}$
Part (b): ${(4 p^{\frac{1}{3}} q^{\frac{1}{2}})}^{\frac{3}{2}}$