Exponent Rules
Simplify the following expression:
a^5/a^2
a^3
True or false:
sqrt(3) is a constant
True
Simplify.
-3c^2d^4(9c^3d^2-4cd^5)
-27c^5d^6+12c^3d^9
Factor completely.
21x^6y^3+9x^3y^3-15x^3y
3x^3y(7x^3y^2+3y^2-5)
Solve.
3x^2+26x+35=0
{-7,-5/3}
Simplify the following expression:
(3a^4b)(6a^5b)
18a^9b^2
True or false:
2/x is a monomial
False
Simplify. Write your answer in standard form.
w(-7w+4)-w(-w^2+4w-1)
w^3-11w^2+5w
Factor completely.
2 x^4-16x
2x(x-2)(x^2+2a+4)
Solve.
4x^3=36x
{-3,0,3}
Simplify the following expression. Use only positive exponents in your final answer.
(10a^7b)/(5a^3b^2)
(2a^4)/b
What is the degree of the following polynomial?
-3x^15-8+2x^22+4x
22
Simplify. Write your answer in standard form.
-2+(x+1)^2
x^2+2x-1
Factor completely.
14x^3+2x^2-14x-2
2(x+1)(x-1)(7x+1)
Solve.
(3x-1)(2x^2-5x+2)=0
{1/3,1/2,2}
Simplify the following expression. Leave your answer in exponential form:
(t^(1/8))(t^(2/5))
t^(21/40)
What is the sum of the coefficients of the following polynomial?
4x^2-2x-x^5+7x^18
8
Simplify. Write your answer in standard form.
(7m-8)(m^2-5m-2)
7m^3-43m^2+26m+16
Factor completely.
x^4-81
(x^2+9)(x+3)(x-3)
Solve.
2x(x-12)=-40
{2,10}
Simplify the following expression:
((-4xy^-5z)/(2xy^3))^-5
-y^40/(32z^5)
Describe the end behavior of the following polynomial:
8x^14-6x-3x^23-6x^51
Leading term: -6x^51
Degree: odd, LC negative
Goes up on the left, down on the right
Simplify. Write your answer in standard form.
-5x^3(x+4)(x^2-5)
-5x^6-20x^5+25x^4+100x^3
Factor completely.
a^4-3a^2+2
(a^2-2)(a+1)(a-1)
Solve.
3x^2+2x=12-7x
{-4,1}
Simplify the following expression:
x^(2a)(y^(b))^3*x^(5a)y^(2b)
x^(7a)y^(5b)
What are the two components that determine the end behavior of a polynomial (include the name and what distinguishes the end behavior)
Degree: even/odd
Leading coefficient: positive/negative
Simplify. Write your answer in standard form.
(5x^2-3x+8)(7x^2-5x-1)
35x^4-46x^3+66x^2-37x-8
Factor completely.
x^5-4x^3+5x^2-20
(x+2)(x-2)(x^3+5)
Solve.
8x^3+10x^2=3x
{-3/2,0,1/4}