Exponent Rules and Polynomials

Simplify

100

(-2)^0

1

200

8^{\frac{2}{3}}

4

300

\frac{12x^{0}z^{-9}}{y^{-3}}

\frac{12y^{3}}{z^{9}}

400

Evaluate when a=3 and b=8

a^{-2}b^{0\ }

\frac{1}{9}

500

Use the product rule for exponents to multiply:

\(a^{6}b^{12})^{\frac{1}{2}}\ 6\sqrt{b^{6}}\ 

a^{3}b^{7}

Random

100

Find the degree of the monomial 

4p^{3}k^{5}

Degree of 8

200

Find the degree of the polynomial 

2p^{4}k^{2}+\frac{1}{2}k^{4}-5

Degree of 5

300

Classify each polynomial according to its degree and number of terms.

-3y^{5}+18y^{3}+9

Quintic Trinomial

400

Classify each polynomial according to its degree and number of terms.

-3y^{2}+18y+9x-10

Quadratic Polynomial

500

A pool is enclosed by a fence that forms a rectangular area. The length of the fence is 4 times more than the width. 

1. Write a polynomial that represents the area enclosed by the fence. DRAW A PICTURE! What is the area when the width is 3 miles??

36 miles

Rules

100

Use the power rule to simplify:

(3x^2y^4)^3

27x^6y^12

200

Use the exponent rules to simplify:

(x^3y^4)^3*(3xy^2)^-2

(x^9y^8)/9

300

Use the quotient rule and the negative exponent rule to simplify:

(2x^2y^4)/(8x^5y^5)

(1)/(4x^3y)

400

Use the quotient rule for exponents to divide:

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

xy^2

500

Use the quotient rule and the negative exponent rule to simplify:

(5x^5y^2z)/(25xy^7z^3)

(x^4)/(5y^5z^2)

Adding & Subtracting Polynomials

100

Add the following polynomials. Write your final answer in standard form.

(4x^2+4)+(19x^2-7)

23x^2-3

200

Add the following polynomials. Write your final answer in standard form.

(13x^2y-2x+1)+(9x^2y-7)

22x^2y-2x-6

300

Add the following polynomials. Write your final answer in standard form.

(-x^3+8x^2-5)+(10x^3-x^2+1)

9x^3+7x^2-4

400

Subtract the following polynomials. Write your final answer in standard form.

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

-8x+8

500

Subtract the following polynomials. Write your final answer in standard form.

(x^2-x+4)-(x^2+x-2)

-2x+6

Multiplying Polynomials

100

Multiply the polynomials. Write your final answer in standard form.

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

-6

200

Multiply the polynomials. Write your final answer in standard form.

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

54x^2+24x+2

300

Multiply the polynomials. Write your final answer in standard form.

(4x-1)^3

16

400

Multiply the polynomials. Write your final answer in standard form.

(7x+4)(7x-4)

49x^2-16

500

Multiply the polynomials. Write your final answer in standard form.

(2x-5)(3x^2-x+6)

6x^3-17x^2+17x-30