1.3 Powers of Powers

Open Ended

Type your answers to the warm up here.

Open Ended

How will you meet the learning target for today?

Math Response

Type answer here

Correct Answer: \left(-3\right)^6

Deg^°

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Open Ended

Why was the answer in Example # 1 positive?

Math Response

Type answer here

Correct Answer: 2^{10}

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Math Response

Type answer here

Correct Answer: \left(\frac{5}{2}\right)^2\times2^6

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Open Ended

For the last example, why was the exponent 2 applied to both of the factors in the first step?

Math Response

Type answer here

Correct Answer: 7^2\times2^4

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Math Response

Type answer here

Correct Answer: 1^4\times0.2

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Open Ended

Example 3: Write about it! Why were the exponents multiplied when simplifying the expression?

Math Response

Type answer here

Correct Answer: \left(\frac{2}{3}\right)^6\times3^9

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Math Response

Type answer here

Correct Answer: \frac{\left(-2\right)^4}{3^4}

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Math Response

Type answer here

Correct Answer: \frac{1^3}{5^{ }}

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Math Response

Type answer here

Correct Answer: 5^2x^6

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Multiple Choice

Simplify:

(b⁵)(b⁴)

• $$2b^{54}$$  

• $$b^{20}$$  

• $$b^9$$  

• $$b$$  

• None of these

Multiple Choice

Simplify:

(r⁴)⁶

• 10r

• r¹⁰

• 24r

• r²⁴

Multiple Choice

Simplify:
(x³)²

• x⁵

• x

• x⁶

• 3x²

Multiple Choice

Simplify:

(5³)⁷

• 5²¹

• 5¹⁰

• 5⁴

• 125²¹

Multiple Choice

Power to a Power Rule

When raising a power to a power, keep the base and ________ the exponents

• postive

• subtract

• multiply

• divide

Multiple Choice

Power of a Product Rule

When raising a product to a power, __________ the exponents to each factor in the product. Then simplify the expression.

• distribute

• add

• multiply

• divide

Multiple Choice

Power of a Quotient Rule

When raising a quotient to a power, distribute the _____________ to the numerator and denominator. Then simplify the expression.

• exponent

• numbers

• integers

• name

Multiple Choice

$$\left(ab^5\right)^7$$  

• $$a^6b^2$$  

• $$a^8b^{12}$$  

• $$ab^{35}$$  

• $$a^7b^{35}$$  

Multiple Choice

$$\left(12n^{14}\right)^{10}$$  

• $$12n^{140}$$  

• $$12^{11}n^{24}$$  

• $$12n^{24}$$  

• $$12^{10}n^{140}$$  

Multiple Choice

$$\left(6qr^4\right)^3$$  

• $$6q^4r^7$$  

• $$6^4q^4r^7$$  

• $$6^3q^3r^{12}$$  

• $$6q^3r^{12}$$  

Multiple Choice

Simplify

• x²⁸y¹² / x²y

• x²⁸y¹² / x⁸y⁴

• x²⁰y⁸

Multiple Choice

• A

• B

• C

• D

Multiple Choice

Simplify:
(12x⁵y⁴/16x²y⁶)^{2
Note: / is divide--rewrite first part over the second part to view easier}

• 9x⁹/16y⁴

• 144x¹⁰y⁸/256x⁴y¹²

• 3x^6/4y⁴

• 9x⁶/16y⁴