Chapter 8: Q. 8.69 (page 784)

Simplify:
a. $\frac{m^{\frac{2}{3}} \cdot m^{\frac{- 1}{3}}}{m^{\frac{- 5}{3}}}$ b. ${(\frac{25 m^{\frac{1}{6}} n^{\frac{11}{6}}}{m^{\frac{2}{3}} n^{\frac{- 1}{6}}})}^{\frac{1}{2}}$

Short Answer

Expert verified

Part (a). The answer is $m^{2}$

part (b). The answer is $\frac{5 n}{m^{\frac{1}{4}}}$ .

Step by step solution

Part (a) Step 1. Simplifying

Use the Product Property in the numerator, add the exponents.

$\frac{m^{\frac{2}{3}} \cdot m^{\frac{- 1}{3}}}{m^{\frac{- 5}{3}}} \frac{m^{\frac{2}{3} - \frac{1}{3}}}{m^{\frac{- 5}{3}}} \frac{m^{\frac{2 - 1}{3}}}{m^{\frac{- 5}{3}}} \frac{m^{\frac{1}{3}}}{m^{\frac{- 5}{3}}}$

Use the Quotient Property, subtract the

exponents,

$\frac{m^{\frac{1}{3}}}{m^{\frac{- 5}{3}}} m^{\frac{1}{3} - (- \frac{5}{3})} m^{\frac{1 + 5}{3}} m^{\frac{6}{3}} m^{2}$

Part (b) Step 1. Simplifying the expression

Follow the order of operations to simplify inside the parentheses first.

Use the Quotient Property, subtract the

exponents.

${(\frac{25 m^{\frac{1}{6}} n^{\frac{11}{6}}}{m^{\frac{2}{3}} n^{\frac{- 1}{6}}})}^{\frac{1}{2}} {(\frac{25 m^{\frac{1}{6} - \frac{2}{3}}}{n^{\frac{- 1}{6} - \frac{11}{6}}})}^{\frac{1}{2}} {(\frac{25 m^{\frac{- 1}{2}}}{n^{- 2}})}^{\frac{1}{2}}$

Use the Product to a Power Property,

multiply the exponents

${(\frac{25 m^{\frac{- 1}{2}}}{n^{- 2}})}^{\frac{1}{2}} \frac{25^{\frac{1}{2}} \cdot m^{\frac{- 1}{2} \cdot \frac{1}{2}}}{n^{- 2 \cdot \frac{1}{2}}} \frac{5 m^{\frac{- 1}{4}}}{n^{- 1}} \frac{5 n}{m^{\frac{1}{4}}}$

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Simplify:
a. $\frac{m^{\frac{2}{3}} \cdot m^{\frac{- 1}{3}}}{m^{\frac{- 5}{3}}}$ b. ${(\frac{25 m^{\frac{1}{6}} n^{\frac{11}{6}}}{m^{\frac{2}{3}} n^{\frac{- 1}{6}}})}^{\frac{1}{2}}$

Short Answer

Step by step solution

Part (a) Step 1. Simplifying

Part (b) Step 1. Simplifying the expression

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Simplify:a.m23·m-13m-53b.25m16n116m23n-1612

Short Answer

Step by step solution

Part (a) Step 1. Simplifying

Part (b) Step 1. Simplifying the expression

One App. One Place for Learning.

Most popular questions from this chapter

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Simplify:
a. $\frac{m^{\frac{2}{3}} \cdot m^{\frac{- 1}{3}}}{m^{\frac{- 5}{3}}}$ b. ${(\frac{25 m^{\frac{1}{6}} n^{\frac{11}{6}}}{m^{\frac{2}{3}} n^{\frac{- 1}{6}}})}^{\frac{1}{2}}$