Laws 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 2⁵ = 32

300

Simplify using the Product Rule:

10^3*10^(-2)

What is 

10^1?

400

Simplify using the Product Rule and Quotient Rule:

(z^5*z^3)/z^2

What is 

z^6?

500

x^3y^5*x^8y^4z

What is 

x^11y^9z?

Power Rule

100

Simplify using the Power Rule:

(m^(3))^4

What is 

m^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:

(3m^4n^5)^2

What is 

9m^8n^10 

500

Simplify using the Power Rule:

(7x^3)^2*(x^4)^(3)

What is 

49x^18?

Add

100

Add the Trinomials:

(5t^2+6t-4)+(3t^2-2t+7)

What is 

8t^2+4t+3?

200

Add:

(3z^4-2z^3+8)+(-2z^4-5z^3+4z^2-z)

What is 

z^4-7z^3+4z^2-z+8?

300

Simplify:

(4a^5+2a^3-4a+5)+(-4a^4-5a^3+6a^2-2)

What is 

4a^5-4a^4-3a^3+6a^2-4a+3?

400

Simplify using the Quotient Rule:

(4x^3+5y^2-3)+(-6x^3+2y^2+8)

What is 

-2x^3+7y^2+5?

500

Simplify using the Quotient Rule:

(8x^3+2x^2-7x+2)+(4x^3+4x-8)

What is 

12x^3+2x^2-3x-6?

Power of a Product

100

Simplify using the Power of a Product Rule:

(2xy^5)^3

What is 

8x^3y^15?

200

Simplify using the Power of a Product Rule:

(5x)^4

What is 

625x^4?

300

Simplify using the Power of a Product Rule:

(7z^2)^3

What is

343z^6?

400

Simplify using the Power of a Product Rule:

(4x^5y^3z)^3

What is 

64x^15y^9z^3?

500

Simplify using the Power of a Product Rule:

((1/3)xz^3)^2

What is 

(1/9)x^2z^6?

Power of a Quotient

100

Simplify using the Power of a Quotient Rule:

(1/2)^3

What is 

1/8?

200

Simplify using the Power of a Quotient Rule:

((3x)/5)^2

What is 

(9x^2)/25?

300

Simplify using the Power of a Quotient Rule:

((6m^3n^5)/(8m^2n^6))^(3)

What is 

(27m^3/64n^3)?

400

Simplify using the Power of a Quotient Rule:

((5n^4*2m^3)/(8n^2))^(4)

What is 

(625m^12n^8)/256

500

Simplify using the Power of a Quotient Rule:

(5^3/(2*5^4x^2))^(2)

What is 

1/(100x^4)?

Subtract

100

Simplify:

(6z^2+8z)-(2z^2-4z)

What is 

4z^2+12z?

200

Subtract:

(4m^2-3m+5)-(2m^2+5m+3)

What is 

2m^2-8m+2?

300

Simplify by subtracting:

(-3m^4+m^3+8)-(m^4+4m^3-6m+5)

What is 

-4m^4-3m^3+6m+3?

400

Simplify using the Zero and Negative Exponent Rules:

(4a^4b^3+5a^3b^4-c^2)-(a^4b^4+3a^3b^4-5a^2b-6c^2)

What is 

4a^4b^3-a^4b^4+2a^3b^4+5a^2b+5c^2?

500

Simplify using the Negative Exponent Rule:

(6x^4y^3z^2+8x^2y^3+2z^2)-(-2x^4y^3z^2+5x^3y^2-7z^2)

What is 

8x^4y^3z^2-5x^3y^2+8x^2y^3+9z^2?