Block Final Review

Exponent Rules

100

What is the simplified form of the expression?

(-1.4)⁰

1

200

What is the simplified form of the expression?

8c²b^-6

8c²/b⁶

300

What is the value of 2x^-3y^-2 for x=2 and y=3

1/36

400

What is the simplified form of the expression?

(-5g⁵)*6h⁸*6g²

-180g⁷h⁸

500

What is the simplified form of the expression?

(a⁹b³)/(a²⁰b^-3)

b⁶/a¹¹

Rational Exponents

100

Simplify the expression.

27^5/3

243

200

Factor the expression.

45x² - 80

5(3x+4)(3x-4)

300

Simplify the expression.

a^-2/a¹⁰

1/a¹²

400

Simplify the following expression. Leave your answer in exponential form. 

(2x^1/3)*(-4x^2/3)*(3x^1/3)

-24x^4/3

500

Simplify the following expression. Leave your answer in exponential form. 

(-2xy^2/5)*(xy^3/4)*(5x^2/3y^1/2)

-10x^8/3y^33/20

Word Problems

100

Suppose an investment of $5200 doubles in value every decade. The function f(x)=5200*2^x gives the value of the investment after x decades. How much is the investment worth after 6 decades?

$332,800

200

Suppose that a square lawn is x²+4x+4. What is the length of one side of the lawn? Use factoring. 

x+2

300

A sports team is building a new stadium on a rectangular lot of land. If the lot measures 5x by 7x and the sports field will be 4x by 3x, how much of the lot will be left over to build bleachers on?

23x

400

A boat costs $15,200 and decreases in value by 8% per year. How much will the boat be worth after 6 years?

$9,216.60

500

Find the balance in the account. 

$4900 principal earning 6%, compounded annually, after 8 years?

$7809.86

Operations with Polynomials

100

Write the polynomial in standard form and name it based on it's degree and number of terms. 

8x+9x³-9

9x³+8x-9

cubic trinomial

200

Simplify the sum. Your answer must be in standard form.

(3x³+3x²+4)+(8x³-5x+8)

11x³+3x²-5x+12

300

Simplify the difference. Your answer must be in standard form. 

(5w²-4w-7)-(6w²+3w-5)

-w²-7w-2

400

Simplify the product. Your answer must be in standard form. 

(3x-7)(3x-5)

9x²-36x+35

500

Simplify the product. Your answer must be in standard form.

(2x+3)(2x²-4x-4) 

4x³-2x²-20x-12

Factoring Polynomials

100

Factor.

x²-13x+36

(x-9)(x-4)

200

Factor.

6x²+5x+1

(3x+1)(2x+1)

300

Factor.

12x³+18x²-10x-15

(6x²-5)(2x+3)

400

Factor.

20x²+22x-12

2(5x-2)(2x+3)

500

Factor.

6x⁴-9x³-36x²+54x

3x(x²-6)(2x-3)