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

Laws of Exponents

Authored by Rachael Threadgill

Mathematics

7th - 9th Grade

CCSS covered

Used 42+ times

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MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Evaluate this expression using the quotient rule.

9⁵

9⁹

1⁵

9^-5

Tags

CCSS.HSA.APR.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Simplify:
b²⋅ b⁴

b⁸

b⁶

b²

2b⁶

Tags

CCSS.6.EE.A.1

CCSS.6.EE.A.3

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Simplify:
(x⁵)⁴

x⁹

x²⁰

x⁵⁴

Tags

CCSS.8.EE.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

(x³y)⁶

2x¹⁸y⁶

x¹⁸y⁶

x³y⁶

Tags

CCSS.HSN.RN.A.2

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Simplify (-1/2)⁰

-1

-2

Tags

CCSS.8.EE.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Simplify the following expression:
xy^-7

xy⁷

x/y⁷

x⁷/y

x⁷y

Tags

CCSS.HSN.RN.A.2

CCSS.HSN.RN.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

n²⋅n⁴⋅n⁵

n¹¹

n⁴⁰

n¹³

n²²

Tags

CCSS.8.EE.A.1

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Laws of Exponents

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n²⋅n⁴⋅n⁵

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