Exponent Rules (Product, Power, Quotient)
Use the product rule for exponents to multiply: 4x3⋅5x2
20x5
Use the zero exponent rule to simplify:
-9x0
-9
Add the following polynomials, write your answer in standard form.
(4x2+4)+(19x2-7)
23x2-3
Multiply the polynomials and write your answer in standard form:
-3x(2x2+4)
-6x3-12x
Determine the degree of the following polynomial:
-3x2+5x-1
2
Use the quotient rule for exponents to divide:
x2y5÷ xy3
xy2
Rewrite using positive exponents:
x-1÷ x-8
x8
Add the following polynomials and write your answer in standard form:
(13x2y-2x+1)+(9x2y-7)
22x2y-2x-6
Multiply the polynomials and write your answer in standard form:
(9x+1)(6x+2)
54x2+24x+2
Is the following a monomial, a binomial, or a trinomial?
2xy-3x2y
Binomial
Use the power rule to simplify:
(4x2yz3)4
16x8y4z12
Use the zero exponent rule to simplify:
(-9x2y)0
1
Add the following polynomials and write your answer in standard form:
(-x3+8x2-5)+(10x3-x2+1)
9x3-7x2-4
Divide the polynomials and write your answer in standard form:
(9x2-3x)÷ 3x
3x-1
How many terms are in the following polynomial?
3x-2xy2-5+y2
4
Use the product rule to multiply:
(2ab2c2)(4a3b5c7)
8a4b7c9
Simplify:
2x2y4 ÷ 8x5y5
1/(4x3y)
Subtract the following polynomials and write your answer in standard form:
(3x+2)-(11x-6)
-8x+8
Multiply the polynomials and write your answer in standard form:
-5c2(15c-4c)
-55c3
Rewrite the polynomial in standard form:
4x-7+3x4-6x2+8x6
8x6+3x4-6x2+4x-7
Use exponent rules to simplify:
(x3y4)3 ⋅ (3xy2)2
9x11y16
Rewrite using only positive exponents:
(a-2b3)÷ (c-4d-1)
(b3c4d)/a2
Subtract the following polynomials and write your answer in standard form:
(3x2-7x+4)-(x2+x-2)
2x2-8x+6
Divide the polynomials and write your answer in standard form:
(-16x2+8x3+2x)÷ 2x
4x2-8x+1
Name the coefficient in front of the variable with the highest degree:
7x+6x5-4x3
6