Vocabulary
Numbers and variables multiplied together
monomials
(a^2)(a^3)
a^5
(x^3) / (x^2)
x
(x^2)^3
x^6
z^0
1
What you do to the exponents when multiplying powers with the same base
addition
(a^4 b^6)(a^2 b^9)
(a^6 b^15)
(a^18 b^10) / (a^8 b^5)
a^ 10 b^5
(a^7 b^9)^5
a^35 b^45
(x^12) (x^-2)
x^10
The number in front of a monomial
coefficients
(x^-2 y^4 z^-2)(x^6 y^4 z^-2)
(x^4 y^8 z^-4)
(x^3 y^5) / (x^-3 y^6)
x^6 y^-1
(2 a^6 b^4)^3
8 a^18 b^12
(a^4 b^3) (a^2 b^2)
(a^6 b^5)
What you do when you are dividing powers with the same base
subtract the exponents
(3a^4 b^3)( a^-5 b)
3 (a^-1 b^4)
(15 x^-4 y^2 z^13) / (3 x^6 y^ -6 z^10)
What is 5 X^-10 y^8 z^3
(3 x^2 y^5 z^-5)^3
27 x^6 y^15 z^-15
(8x^-3 y^4)(2x^-4 y^2)
16x^-7 y^6
What you multiply when a power is raised to a power
exponents
(-12 w^-4 x^19 y^2 z^-5)(-3w^4 x^-9 y^3)
(36 x^10 y^5z^-5)
(25 x^-5 y^17) / (5 x^ 15 y^-3)
5 x^-20 y^20
(5 x^-6 x^3 y^5 z^3)^5
125 x^-15 y^25 z^15
The "degree" of a polynomial
The largest exponent