Laws of Exponents

First Law of Exponents (Product Rule)

100

Simplify using the product rule: 

a^2*a^3

What is 

a^5?

200

Simplify using the product rule:

2^4*2

What is 

2^5?

300

Simplify using the Product Rule:

10^3*10^(-2)

What is 

10^1?

400

Simplify using the Product Rule:

3^8*27

Hint: Rewrite 27 as 3 raised to a power to simplify

What is 

3^11?

500

x^3*x^(-17)=x^n

Find the value of n.

What is 

n=-14?

Second Law of Exponents (Quotient Rule)

100

Simplify using the Quotient Rule:

2^5/2^3

What is 

2^2?

200

Simplify using the Quotient Rule:

z^4/z

What is 

z^3?

300

Simplify using the Quotient Rule:

3^12/3^8

What is 

3^4?

400

Simplify using the Quotient Rule:

(10x^7)/(2x^4)

What is 

5x^3?

500

Simplify using the Quotient Rule:

(54x^9y^8)/(6x^3y^4)

What is 

9x^6y^4

Third Law of Exponents (Power of a Power Rule)

100

Simplify using the Power Rule:

(2^(3))^4

What is 

2^12?

200

Simplify using the Power Rule:

(x^3)^2

What is 

x^6?

300

Simplify using the Power Rule:

(b^5)^(-3)

What is 

b^(-15)?

400

Simplify using the Power Rule:

(11^2)^-2

What is 

11^(-4)?

500

Simplify using the Power Rule:

(7x^3)^2

What is 

7^2*x^6?

Fourth Law of Exponents (Power of a Product Rule)

100

Simplify using the Power of a Product Rule:

(2x)^3

What is 

2^3x^3?

200

Simplify using the Power of a Product Rule:

(10^2)^2

What is 

10^4?

300

Simplify using the Power of a Product Rule:

(7^3z^2)^3

What is

7^9z^6?

400

Simplify using the Power of a Product Rule:

(3^5x^2)^4

What is 

3^20x^8?

500

Simplify using the Power of a Product Rule:

(1/3xz)^2

What is 

(1/3)^2x^2z^2?

Fifth Law of Exponents (Power of a Quotient Rule)

100

Simplify using the Power of a Quotient Rule:

(1/2)^3

What is 

(1^3)/2^3?

200

Simplify using the Power of a Quotient Rule:

((3x)/5)^2

What is 

(3^2x^2)/5^2?

300

Simplify using the Power of a Quotient Rule:

(6/7)^(-5)

What is 

(6^-5/7^-5) = (7^5/6^5)?

400

Simplify using the Power of a Quotient Rule:

(3^2/8^3)^5

What is 

3^10/8^15?

500

Simplify using the Power of a Quotient Rule:

(5^-3/(2x^2))^(5y)

What is 

(5^(-15y))/(2^(5y)x^(10y)) = 1/(5^(15y)2^(5y)x^(10y))?

Zero and Negative Exponents Rule

100

Simplify using the Zero Exponent Rule:

a*b^0

What is 

a*1?

200

Simplify using the Negative Exponent Rule:

3^-2

What is 

1/3^2?

300

Simplify using the Negative Exponent Rule:

(1/2^-3)

What is 

2^3?

400

Simplify using the Zero and Negative Exponent Rules:

(7^3x^4)^0

What is 

1?

500

Simplify using the Negative Exponent Rule:

7/(x^-3y^5)

What is 

(7x^3)/y^5?