Chapter 7: Q13. (page 404)

Simplify the expression
${(4 a^{4} b^{9} c)}^{2}$

Short Answer

Expert verified

The simplified version of ${(4 a^{4} b^{9} c)}^{2}$ is $16 a^{8} b^{18} c^{2}$ .

Step by step solution

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

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

In general: ${(x y)}^{m} = x^{m} y^{m}$

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.

In general: ${(x^{m})}^{n} = x^{m \times n}$

Step 3. Simplify the expression.

The given expression is: ${(4 a^{4} b^{9} c)}^{2}$

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

${(4 a^{4} b^{9} c)}^{2} = {(4)}^{2} {(a^{4})}^{2} {(b^{9})}^{2} {(c)}^{2}$

Apply the ‘Law of indices’ for power of index numbers and simplify further.

${(4 a^{4} b^{9} c)}^{2} = {(4)}^{2} {(a^{4})}^{2} {(b^{9})}^{2} {(c)}^{2} = 16 (a^{4 \times 2}) (b^{9 \times 2}) (c^{2}) = 16 (a^{8}) (b^{18}) (c^{2}) = 16 a^{8} b^{18} c^{2}$

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Simplify the expression
${(4 a^{4} b^{9} c)}^{2}$

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 expression4a4b9c2

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

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Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

Simplify the expression
${(4 a^{4} b^{9} c)}^{2}$