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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 7: Q3B. (page 403)

Simplify the expression
${[{(3^{2})}^{3}]}^{2}$

Short Answer

Expert verified

The simplified version of ${[{(3^{2})}^{3}]}^{2}$ is 531441.

Step by step solution

01

Step 1. 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: ${(x^{m})}^{n} = x^{m 脳 n}$

02

Step 2. Simplify the expression.

Apply the brackets rule and simplify the given expression.

${[{(3^{2})}^{3}]}^{2} = {[3^{2 脳 3}]}^{2} = {[3^{6}]}^{2} = 3^{6 脳 2} = 3^{12} = 531441$

03

Step 3. State the conclusion.

Thus the simplification of ${[{(3^{2})}^{3}]}^{2}$ is 531441.

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Most popular questions from this chapter

Simplify the expression

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