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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: Q3A. (page 403)

Simplify the expression
${[{(2^{2})}^{2}]}^{4}$

Short Answer

Expert verified

The simplified version of ${[{(2^{2})}^{2}]}^{4}$ is 65536.

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.

${[{(2^{2})}^{2}]}^{4} = {[2^{2 脳 2}]}^{4} = {[2^{4}]}^{4} = 2^{4 脳 4} = 2^{16} = 65536$

03

Step 3. State the conclusion.

Thus the simplification of ${[{(2^{2})}^{2}]}^{4}$ is 65536.

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Most popular questions from this chapter

Find each product.

$a (a^{2} + 2 a 鈭� 10)$

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$(2 a 鈭� 5) (3 a + 5)$

MULTIPLE CHOICE Antonia is carpeting two of the rooms in her house. The dimensions are shown. What is the total area to be carpeted?

F $x^{2} + 3 x$

G $2 x^{2} + 6 x 鈭� 10$

H $x^{2} + 3 x 鈭� 5$

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Read each question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.

Mickey has $180$ feet of fencing that she wants to use to enclose a play area for her puppy. She will use her house as one of the sides of the region.

If she makes the play area $x$ feet deep as shown in the figure, write a polynomial in standard form to represent the area of the region.
How many square feet of area will the puppy have to play in if Mickey makes it $40$ feet deep?

Evaluate each product or quotient. Express the results in scientific notations.

$\frac{8.8 脳 10^{2}}{4 脳 10^{鈭� 4}}$

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