Chapter 7: Q12. (page 404)

Simplify the expression
${(x y^{4})}^{6}$

Short Answer

Expert verified

The simplified version of ${(x y^{4})}^{6}$ is $x^{6} y^{24}$ .

Step by step solution

Step 1. State the product power law of ‘laws of indices’.

According to this lawwhen a product is raised to a power, every factor of the product is raised to the power.

That is, ${(x y)}^{m} = x^{m} y^{m}$

Step 2. State the ‘Law of indices’ for power of index numbers.

If a term with a power is itself raised to a power then the powers are multiplied together.

That is, ${(x^{m})}^{n} = x^{m \times n}$

Step 3. Simplify the expression.

The given expression is: ${(x y^{4})}^{6}$

First apply the product power law to simplify the given expression.

${(x y^{4})}^{6} = (x^{6}) {(y {}^{4})}^{6}$

Apply the ‘Law of indices’ for power of index numbers in width="42" height="24" role="math">y46 and simplify further.

${(x y^{4})}^{6} = (x^{6}) {(y {}^{4})}^{6} = (x^{6}) (y^{4 \times 6}) = (x^{6}) (y^{24}) = x^{6} y^{24}$

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Simplify the expression
${(x y^{4})}^{6}$

Short Answer

Step by step solution

Step 1. State the product power law of ‘laws of indices’.

Step 2. State the ‘Law of indices’ for power of index numbers.

Step 3. Simplify the expression.

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Simplify the expressionxy46

Short Answer

Step by step solution

Step 1. State the product power law of ‘laws of indices’.

Step 2. State the ‘Law of indices’ for power of index numbers.

Step 3. Simplify the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

Probability and Statistics

Statistics

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Simplify the expression
${(x y^{4})}^{6}$