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

Step 1. Define an expression.

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

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.

Step 3. Simplify the expression 3xy32z3.

Use the property of power of a power rule.

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

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

Short Answer

Step by step solution

Step 1. Define an expression.

Step 2. Define power of a power rule.

Step 3. Simplify the expression 3xy32z3.

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Simplify the given expression. Assume that no denominator equals zero.3xy32z3

Short Answer

Step by step solution

Step 1. Define an expression.

Step 2. Define power of a power rule.

Step 3. Simplify the expression 3xy32z3.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Mechanics Maths

Pure Maths

Discrete Mathematics

Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.

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