Exponents and Polynomials

Exponent Rules (Product, Power, Quotient)

100

Use the product rule for exponents to multiply: 4x³⋅5x²

20x⁵

200

Use the quotient rule for exponents to divide: 

x²y⁵÷ xy³

xy²

300

Use the power rule to simplify:

(4x²yz³)⁴

16x⁸y⁴z¹²

400

Use the product rule to multiply:

(2ab²c²)(4a³b⁵c⁷)

8a⁴b⁷c⁹

500

Use exponent rules to simplify: 

(x³y⁴)³ ⋅ (3xy²)²

9x¹¹y¹⁶

Exponent Rules (Negative, Zero)

100

Use the zero exponent rule to simplify:

-9x⁰

-9

200

Simplify using only positive exponents.

(3x^-8)/(3x^2)

1/(x^10)

300

Simplify:

(-9x²y)⁰

1

400

Simplify:

2x^2y^4 * 8x^5y^-5

(16x^7)/y

500

Rewrite using only positive exponents:

(a^-2b^3)/(c^-4d^-1)

(b^3c^4d)/(a^2)

Adding, Subtracting, & Multiplying Polynomials

100

Write your answer in standard form:

(13x²-2x+1)+(9x²-7)

22x²-2x-6

200

Write your answer in standard form:

(3x+2)-(11x-6)

-8x+8

300

Write your answer in standard form:

(3x²-7x+4)-(x²+x-2)

2x²-8x+6

400

Write your answer in standard form:

-3x(2x²+4)

-6x³-12x

500

Write your answer in standard form:

(9x+1)(6x-2)

54x²-12x-2

Factoring Polynomials

100

x^2+16x+28

(x+14)(x+2)

200

x²-13x+36

(x-9)(x-4)

300

x²-900

(x+30)(x-30)

400

3x²+36x+96

3(x+8)(x+4)

500

-2x²-52x+240

-2(x+30)(x-4)

Factoring Polynomials

100

x²+x-30

(x+6)(x-5)

200

x²-22x-75

(x-25)(x+3)

300

x²-196

(x+14)(x-14)

400

10x²-160x+640

10(x-8)(x-8) or 10(x-8)²

500

4x³-40x²-300x

4x(x-15)(x+5)