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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 7: Q21. (page 460)

Simplify the given expression. Assume that no denominator equals zero.
${(\frac{3 x y^{3}}{2 z})}^{3}$

Short Answer

Expert verified

The final expression is $\frac{216 x^{3} y^{9}}{z^{3}}$ .

Step by step solution

01

Step 1. Define an expression.

A mathematical expression is a combinations of numbers and variables ordered with mathematical operations.

02

Step 2. Define power of a power rule.

The power of a power rule states that if a base raised to a power is being raised to another power, the exponents are multiplied and the base remains the same.

${(x^{m})}^{n} = x^{m n}$

Where, $x$ is any non-zero real number.

03

Step 3. Simplify the expression 3xy32z3.

Use the property of power of a power rule.

${(\frac{12 x y^{3}}{2 z})}^{3} = \frac{{(12 x y^{3})}^{3}}{{(2 z)}^{3}} = \frac{{(12)}^{3} {(x)}^{3} {(y^{3})}^{3}}{{(2)}^{3} {(z)}^{3}} = \frac{1728 (x^{3}) (y^{3 脳 3})}{8 z^{3}} = \frac{216 x^{3} y^{9}}{z^{3}}$

Hence, ${(\frac{12 x y^{3}}{2 z})}^{3} = \frac{216 x^{3} y^{9}}{z^{3}}$

Therefore the final expression is $\frac{216 x^{3} y^{9}}{z^{3}}$ .

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