Chapter 8: Q. 8.70 (page 784)

Simplify:
a. $\frac{u^{\frac{4}{5}} \cdot u^{\frac{- 2}{5}}}{u^{\frac{- 13}{5}}}$ b. ${(\frac{27 x^{\frac{4}{5}} y^{\frac{1}{6}}}{x^{\frac{1}{5}} y^{\frac{- 5}{6}}})}^{\frac{1}{3}}$

Short Answer

Expert verified

Part (a). The answer is $u^{3}$

Part (b). The answer is $3 x^{\frac{1}{5}} y$

Step by step solution

Part (a) Step 1. Simplifying the expression

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

$\frac{u^{\frac{4}{5}} \cdot u^{\frac{- 2}{5}}}{u^{\frac{- 13}{5}}} \frac{u^{\frac{4}{5} - \frac{2}{5}}}{u^{\frac{- 13}{5}}} \frac{u^{\frac{2}{5}}}{u^{\frac{- 13}{5}}}$

Use the Quotient Property, subtract the

exponents,

$\frac{u^{\frac{2}{5}}}{u^{\frac{- 13}{5}}} u^{\frac{2}{5} - (\frac{- 13}{5})} u^{\frac{2 + 13}{5}} u^{\frac{15}{5}} u^{3}$

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.

${(\frac{27 x^{\frac{4}{5}} y^{\frac{1}{6}}}{x^{\frac{1}{5}} y^{\frac{- 5}{6}}})}^{\frac{1}{3}} {(\frac{27 x^{\frac{4}{5} - \frac{1}{5}}}{y^{\frac{- 5}{6} - \frac{1}{6}}})}^{\frac{1}{3}} {(\frac{27 x^{\frac{3}{5}}}{y^{- 1}})}^{\frac{1}{3}}$

Use the Product to a Power Property,

multiply the exponents.

${(\frac{27 x^{\frac{3}{5}}}{y^{- 1}})}^{\frac{1}{3}} \frac{27^{\frac{1}{3}} \cdot x^{\frac{3}{5} \cdot \frac{1}{3}}}{y^{- 1}} 3 x^{\frac{1}{5}} y$

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Simplify:
a. $\frac{u^{\frac{4}{5}} \cdot u^{\frac{- 2}{5}}}{u^{\frac{- 13}{5}}}$ b. ${(\frac{27 x^{\frac{4}{5}} y^{\frac{1}{6}}}{x^{\frac{1}{5}} y^{\frac{- 5}{6}}})}^{\frac{1}{3}}$

Short Answer

Step by step solution

Part (a) Step 1. Simplifying the expression

Part (b) Step 1. Simplifying the expression

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Simplify:a.u45·u-25u-135b.27x45y16x15y-5613

Short Answer

Step by step solution

Part (a) Step 1. Simplifying the expression

Part (b) Step 1. Simplifying the expression

One App. One Place for Learning.

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Simplify:
a. $\frac{u^{\frac{4}{5}} \cdot u^{\frac{- 2}{5}}}{u^{\frac{- 13}{5}}}$ b. ${(\frac{27 x^{\frac{4}{5}} y^{\frac{1}{6}}}{x^{\frac{1}{5}} y^{\frac{- 5}{6}}})}^{\frac{1}{3}}$