Chapter 8: Q. 8.68 (page 783)

Simplify:
a. ${(81 n^{\frac{2}{5}})}^{\frac{3}{2}}$ b. ${(a^{\frac{3}{2}} b^{\frac{1}{2}})}^{\frac{4}{3}}$

Short Answer

Expert verified

Part (a). The answer is $729 n^{\frac{3}{5}}$ .

Part (b). The answer is $a^{2} b^{\frac{2}{3}}$ .

Step by step solution

Part (a) Step 1. Simplifying

First, we use the Product to a Power Property.

So,

${(81)}^{\frac{3}{2}} . {(n^{\frac{2}{5}})}^{\frac{3}{2}}$

To raise a power to a power, we multiply the exponents.

${(81)}^{\frac{3}{2}} \cdot {(n^{\frac{2}{5}})}^{\frac{3}{2}} 3^{4 \cdot \frac{3}{2}} \cdot n^{\frac{2}{5} \cdot \frac{3}{2}} 3^{6} \cdot n^{\frac{3}{5}} 729 n^{\frac{3}{5}}$

Part (b) Step 1. Simplifying the exponent

First, we use the Product to a Power

Property.

So,

${(a^{\frac{3}{2}} b^{\frac{1}{2}})}^{\frac{4}{3}} a^{\frac{3}{2} \cdot \frac{4}{3}} b^{\frac{1}{2} \cdot \frac{4}{3}} a^{2} b^{\frac{2}{3}}$

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Simplify:
a. ${(81 n^{\frac{2}{5}})}^{\frac{3}{2}}$ b. ${(a^{\frac{3}{2}} b^{\frac{1}{2}})}^{\frac{4}{3}}$

Short Answer

Step by step solution

Part (a) Step 1. Simplifying

Part (b) Step 1. Simplifying the exponent

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Simplify:a.81n2532b.a32b1243

Short Answer

Step by step solution

Part (a) Step 1. Simplifying

Part (b) Step 1. Simplifying the exponent

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Simplify:
a. ${(81 n^{\frac{2}{5}})}^{\frac{3}{2}}$ b. ${(a^{\frac{3}{2}} b^{\frac{1}{2}})}^{\frac{4}{3}}$