Quiz Review: Exponents, Factoring, Rational Expressions

Exponent Rules

100

Simplify x⁶ * x^-2

x⁴

200

Simplify (x⁷ * x^-3)/x^-1

x⁵

300

Simplify (-4m)³/10m^-5

-32m⁸/5

400

Simplify (4x)⁰y³/x^-3y

y²x³

500

Simplify (2c^-4d⁵)^-5/4c³d

c¹⁷/128d²⁶

Operations with Polynomials

100

Simplify (11x-5) + (3x - 14)

14x - 19

200

Simplify (1 - 7a) - (7a - 16)

-14a + 16

300

Simplify (7y³ + 16y² - 14) - (8y³ - 5y - 11)

-y³ + 16y² + 5y - 3

400

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

-54m

500

Simplify (n + 4)² * (3n² - 7n + 1)

3n⁴ + 17n³ - 7n² - 104n + 16

Factoring

100

Factor out the GCF -18a³b + 27a²b

-9a²b(2a - 3)

200

Factor 9k² - 64

(3k - 8)(3k + 8)

300

Factor 1 - 125k³

(1 - 5k)(1 + 5k + 25k²)

400

Factor 5k² - 16k + 12

(k - 2)(5k - 6)

500

Factor 4m³ - 12m + 3m - 9

(4m² + 3)(m - 3)

Multiplying/Dividing Rational Expressions

100

Find the product and give your answer in simplest form

[59n/99] * [80/33n]

4720/3267

200

Find the product and give your answer in simplest form

[(20a² - 100a)/(a - 1)] * [2/(16a³ - 80a²)]

5/(2a(a-1))

300

Find the product and give your answer in simplest form

[(4w² - 11w - 3)/(16w² - 1)]  * [(8w - 2)/(9 - w²)]

-2/(3+w)

400

Find the quotient and give your answer in simplest form

[(k⁴ - 16)/(2k² - k - 6)] ÷ [(4k³ + 16k)/(12k² + 18k)]

3(k+2)/2

500

Find the quotient and give your answer in simplest form

[(2m² + 3m)/(2m² - 7m - 15)] ÷ [(8m² + 12m)/(m² - 25)]

(m + 5)/4(2m + 3)

Adding/Subtracting Rational Expressions

100

Find the sum and give your answer in simplest form

[7/x] + [3/x²]

(7x + 3)/x²

200

Find the difference and give your answer in simplest form

[x/(x + 5)] - [2/(x - 3)]

(x² - 5x - 10)/[(x + 5)(x - 3)]

300

Find the sum and give your answer in simplest form

[(6/(x - 2)] + [(x + 3)/(2 - x)]

(-x + 3)/(x - 2)

400

Find the difference and give your answer in simplest form

[r/(r² - 9)] - [1/(r² + 8r + 15)]

(r + 1)/[(r + 5)(r - 3)]

500

Find the sum: a/b + c/d

(ad + bc)/bd