Q14. Simplify the expression聽鈭�2f2g... [FREE SOLUTION]

91影视

Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 7: Q14. (page 404)

Simplify the expression
${(鈭� 2 f^{2} g^{3} h^{2})}^{3}$

Short Answer

Expert verified

The simplified version of ${(鈭� 2 f^{2} g^{3} h^{2})}^{3}$ is $鈭� 8 f^{6} g^{9} h^{6}$ .

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: ${(x^{m})}^{n} = x^{m 脳 n}$

Step 3. Simplify the expression.

The given expression is: ${(鈭� 2 f^{2} g^{3} h^{2})}^{3}$

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

${(鈭� 2 f^{2} g^{3} h^{2})}^{3} = (鈭� 2^{3}) {(f^{2})}^{3} {(g^{3})}^{3} {(h^{2})}^{2}$

Apply the 鈥楲aw of indices鈥� for power of index numbers and simplify further.

${(鈭� 2 f^{2} g^{3} h^{2})}^{3} = {(鈭� 2)}^{3} {(f^{2})}^{3} {(g^{3})}^{3} {(h^{2})}^{3} = (鈭� 8) (f^{2 脳 3}) (g^{3 脳 3}) (h^{2 脳 3}) = (鈭� 8) (f^{6}) (g^{9}) (h^{6}) = 鈭� 8 f^{6} g^{9} h^{6}$

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91影视

Simplify the expression
${(鈭� 2 f^{2} g^{3} h^{2})}^{3}$

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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91影视

Simplify the expression鈭�2f2g3h23

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

Logic and Functions

Mechanics Maths

Theoretical and Mathematical Physics

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Pure Maths

Study anywhere. Anytime. Across all devices.

Simplify the expression
${(鈭� 2 f^{2} g^{3} h^{2})}^{3}$