Properties of Exponents

What's the rule?

100

What is the rule that was applied here?  

  x⁴

 ___         = x²

  x²

Quotient (division)

200

What is the rule that was applied?

(x³)⁴  = x¹²

Power to a power

300

What is the rule that was applied here?

(x⁵)⁵  = x²⁵

Power to a power

400

What is the rule that was applied here?

4⁴ * 4²  = 4⁶

Multiplicative

500

What are the two rules that were applied?

(5⁷)⁴

^{______                    =} 5²⁶

5²

Power to a power and quotient

Multiplicative

100

Simplify using the multiplicative property:

3⁶ * 3²

3⁸

200

Simplify using the multiplicative property:

x⁵ * x⁵

x¹⁰

300

Simplify using the multiplicative property:

5³ * 5¹⁰

5¹³

400

Simplify using the multiplicative property:

y⁴*y²¹*y²

y²⁷

500

Simplify using the multiplicative property:

x³y⁴ * x⁵y⁷

x¹⁵y²⁸

Power to a Power

100

Simplify using the power to a power property:

(x²)³

x⁶

200

Simplify using the power to a power property:

(7⁴)⁵

7²⁰

300

Simplify using the power to a power property:

(x¹⁰)⁶

x⁶⁰

400

Simplify using the power to a power property:

((y⁶)⁴)²

y⁴⁸

500

Simplify using the power to a power property:

(x⁴)² * (y⁶)³

x⁸y¹⁸

Quotient

100

Simplify using the quotient (division) property:

x⁶

^___

x⁴

x²

200

Simplify using the quotient (division) property:

6⁷

___

6⁴

6³

300

Simplify using the quotient (division) property:

x²

___

x⁴

1

__

x²

400

Simplify using the quotient (division) property:

x³y⁵

^_____

x²y

xy⁴

500

Simplify using the quotient (division) property:

x⁴y⁷

____

x⁸y³

y⁴

___

x⁴

Multi-Step

100

Simplify:

(x⁶)³

____

x⁷

x¹¹

200

Simplify:

5³*5⁵

_____

5⁶

5²

300

Simplify:

(a⁴)⁹*(b³)²

a³⁶b⁶

400

Simplify:

(x⁵)⁴ y³z⁴

________

x⁶y²z

x¹⁴yz³

500

Simplify:

(a^b)^c

_____

a^d*a^e

a^bc-(d+e)