Which of the following is the correct way to simplify this expression? ( a m b n ) p \left(a^mb^n\right)^p ( a m b n ) p

a m ⋅ p b n ⋅ p a^{m\cdot p}\ b^{n\cdot p} a m ⋅ p b n ⋅ p

a b m ⋅ n ⋅ p ab^{m\cdot n\cdot p} a b m ⋅ n ⋅ p

Which of the following is the correct way to simplify this expression? ( a m b n ) p \left(\frac{a^m}{b^n}\right)^p ( b n a m ) p

a m ⋅ p b n ⋅ p \frac{a^{m\cdot p}}{b^{n\cdot p}} b n ⋅ p a m ⋅ p

a m + a p b n + b p \frac{a^m+a^p}{b^n+b^p} b n + b p a m + a p

a m ⋅ p b n ⋅ p a^{m\cdot p}\ b^{n\cdot p} a m ⋅ p b n ⋅ p

What's our "shortcut" for thinking of this property? ( a m b n ) p = a m p b n p \left(\frac{a^m}{b^n}\right)^{p\ }=\ \frac{a^{mp}}{b^{np}} ( b n a m ) p = b n p a m p

It's like "distributing" the power to each part of the top and bottom

We subtract m and n, then multiply by p

Power of a Quotient

Authored by Sarah Cuddihy

Other

8th - 9th Grade

CCSS covered

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MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Division Law states: keep the base the same and do this to the exponents.

multiply

add

subtract

divide

Tags

CCSS.8.EE.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

(5²)³

5⁶

5⁵

5⁷

5⁸

Tags

CCSS.6.EE.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

True or False?

True

False

Tags

CCSS.8.EE.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

3.) Simplify
(45x⁶y⁹) ÷ (5x⁴y²)

9x²y⁷

40x²y⁷

9x²/y⁷

9x¹⁰y¹¹

Tags

CCSS.HSA.APR.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Which of the following is the correct way to simplify this expression?
$\left(a^mb^n\right)^p$

$ab^{m\cdot n\cdot p}$

$a^{m\cdot p}\ b^{n\cdot p}$

$a^mb^n$

Tags

CCSS.8.EE.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

What's our "shortcut" for thinking of this property?
$\left(a^mb^n\right)^p\ =\ a^{mp}\ b^{np}$

It's like "distributing" the power

We add the powers together

We divide the powers

Tags

CCSS.8.EE.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Simplify the following:
$\left(r^7s^3\right)^3$

$r^7s^9$

$r^{21}s^9$

$r^{21}s^3$

Tags

CCSS.8.EE.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Simplify the following:
$\left(abc^5\right)^5$

$a^5b^5c^{25}$

$a^5b^5c^5$

$abc^{25}$

Tags

CCSS.8.EE.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Simplify the following:
$\left(4x^3y^2\right)^2$

$16x^3y^2$

$4x^6y^4$

$16x^6y^4$

Tags

CCSS.HSA.APR.A.1

10.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Which of the following is the correct way to simplify this expression?
$\left(\frac{a^m}{b^n}\right)^p$

$\frac{a^{m\cdot p}}{b^{n\cdot p}}$

$\frac{a^m+a^p}{b^n+b^p}$

$a^{m\cdot p}\ b^{n\cdot p}$

Tags

CCSS.8.EE.A.1

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Power of a Quotient

Division Law states: keep the base the same and do this to the exponents.

(52)3

True or False?

3.) Simplify(45x6y9) ÷ (5x4y2)

Which of the following is the correct way to simplify this expression? (ambn)p\left(a^mb^n\right)^p(ambn)p

What's our "shortcut" for thinking of this property? (ambn)p = amp bnp\left(a^mb^n\right)^p\ =\ a^{mp}\ b^{np}(ambn)p = amp bnp

Simplify the following: (r7s3)3\left(r^7s^3\right)^3(r7s3)3

Simplify the following: (abc5)5\left(abc^5\right)^5(abc5)5

Simplify the following: (4x3y2)2\left(4x^3y^2\right)^2(4x3y2)2

Which of the following is the correct way to simplify this expression? (ambn)p\left(\frac{a^m}{b^n}\right)^p(bnam​)p

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(5²)³

3.) Simplify
(45x⁶y⁹) ÷ (5x⁴y²)

Which of the following is the correct way to simplify this expression?
$\left(a^mb^n\right)^p$

What's our "shortcut" for thinking of this property?
$\left(a^mb^n\right)^p\ =\ a^{mp}\ b^{np}$

Simplify the following:
$\left(r^7s^3\right)^3$

Simplify the following:
$\left(abc^5\right)^5$

Simplify the following:
$\left(4x^3y^2\right)^2$

Which of the following is the correct way to simplify this expression?
$\left(\frac{a^m}{b^n}\right)^p$