Chapter 8: Q. 144 (page 787)

In the following exercises, write with a rational exponent.
$(a) \sqrt[3]{a} (b) (\sqrt[4]{21 v})^{3} (c) \sqrt[4]{{(\frac{2 x y}{5 z})}^{2}}$

Short Answer

Expert verified

(a) The answer is $a^{\frac{1}{3}}$

(b) The answer is ${(21 v)}^{\frac{3}{4}}$

Step by step solution

Step 1. Part (a) Simplify the expression a3

We will use the property

$a^{\frac{m}{n}} = (\sqrt[n]{a})^{m}$ and $a^{\frac{m}{n}} = \sqrt[n]{a^{m}}$

$\sqrt[3]{a} = {(a)}^{\frac{1}{3}}$

Step 2. Part (b) Simplify the expression 21v43

${(\sqrt[4]{21 v})}^{3} = {(21 v)}^{3 \times \frac{1}{4}} = {(21 v)}^{\frac{3}{4}}$

Step 3. Part (c) Simplify the expression 2xy5z24

$\sqrt[4]{{(\frac{2 x y}{5 z})}^{2}} = {(\frac{2 x y}{5 z})}^{2 \times \frac{1}{4}} = {(\frac{2 x y}{5 z})}^{\frac{1}{2}}$

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In the following exercises, write with a rational exponent.
$(a) \sqrt[3]{a} (b) (\sqrt[4]{21 v})^{3} (c) \sqrt[4]{{(\frac{2 x y}{5 z})}^{2}}$

Short Answer

Step by step solution

Step 1. Part (a) Simplify the expression a3

Step 2. Part (b) Simplify the expression 21v43

Step 3. Part (c) Simplify the expression 2xy5z24

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In the following exercises, write with a rational exponent.(a)a3(b)(21v4)3(c)2xy5z24

Short Answer

Step by step solution

Step 1. Part (a) Simplify the expression a3

Step 2. Part (b) Simplify the expression 21v43

Step 3. Part (c) Simplify the expression 2xy5z24

One App. One Place for Learning.

Most popular questions from this chapter

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Decision Maths

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In the following exercises, write with a rational exponent.
$(a) \sqrt[3]{a} (b) (\sqrt[4]{21 v})^{3} (c) \sqrt[4]{{(\frac{2 x y}{5 z})}^{2}}$