Chapter 7: Q25. (page 460)

Simplify the given expression. Assume that no denominator equals zero.
$\frac{{(3 x^{- 1})}^{- 2}}{{(3 x^{2})}^{- 2}}$

Short Answer

Expert verified

The final expression is $x^{6}$ .

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. Define quotient of power rule.

The quotient of power rule is given by

$\frac{a^{m}}{a^{n}} = a^{m - n}$

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

Step 4. Simplify the expression 3x−1−23x2−2.

Use the property of power of a power rule.

$\frac{{(3 x^{- 1})}^{- 2}}{{(3 x^{2})}^{- 2}} = \frac{{(3)}^{- 2} {(x^{- 1})}^{- 2}}{{(3)}^{- 2} {(x^{2})}^{- 2}} = \frac{{(x^{- 1})}^{- 2}}{{(x^{- 1})}^{- 2}} = \frac{x^{- 1 (- 2)}}{x^{2 (- 2)}} = \frac{x^{2}}{x^{- 4}}$

Use the property of quotient of power rule.

$\begin{matrix} \frac{x^{2}}{x^{- 4}} = x^{2 - (- 4)} \\ = x^{2 + 4} \\ = x^{6} \end{matrix}$

Hence, $\frac{{(3 x^{- 1})}^{- 2}}{{(3 x^{2})}^{- 2}} = x^{6}$

Therefore the final expression is $x^{6}$ .

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Simplify the given expression. Assume that no denominator equals zero.
$\frac{{(3 x^{- 1})}^{- 2}}{{(3 x^{2})}^{- 2}}$

Short Answer

Step by step solution

Step 1. Define an expression.

Step 2. Define power of a power rule.

Step 3. Define quotient of power rule.

Step 4. Simplify the expression 3x−1−23x2−2.

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Simplify the given expression. Assume that no denominator equals zero.3x−1−23x2−2

Short Answer

Step by step solution

Step 1. Define an expression.

Step 2. Define power of a power rule.

Step 3. Define quotient of power rule.

Step 4. Simplify the expression 3x−1−23x2−2.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Calculus

Pure Maths

Geometry

Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

Simplify the given expression. Assume that no denominator equals zero.
$\frac{{(3 x^{- 1})}^{- 2}}{{(3 x^{2})}^{- 2}}$