Exponent rules & polynomial operations

laws of exponents

100

(5x⁷)²

25x¹⁴

200

(2a²)³+(a⁴)(3a²)

11a⁶

300

c^-2d^-1

____

c⁷d^-2

d

__

c^-9

400

(4x³y⁶)^-2+(2x²y⁴)^-3

3

___

16x⁶y¹²

500

(-6x⁴y⁶)²

________

(-4x^-3y⁵)³

-9x¹⁷

_____

16y³

add & subtract Polynomials

100

(x+5)+(4x-7)

5x-2

200

(8-p²+5p)+(p²-15-4p)

p-7

300

(5r-2s)-(9r-11s)

-4r+9s

400

(3m²+7m-1)-(m²+2m-5)

2m²+5m+4

500

(7v-v²+14)-(15+8v+v²)

-2v²-v-1

divide polynomials by Monomials

100

10v²+5v-15

___________

5

2v²+V-3

200

6a²b-12ab²

_________

-2ab

-3a+6b

300

12c⁵d⁴+18c⁴d³

____________

3c²d³

4c³d+6c²

400

15x⁵-25x³+5x²

____________

5x⁴

3x - 5/x + 1/x²

500

30r⁵s⁹-12r⁴s⁸+3r³s⁷

________________

3r²s²

10v³s⁷-4r²s⁶+rs⁵

multiply polynomials

100

x(x²-x+3)

x³-x²+3x

200

10m⁴n(-2mn³+3n)

-20m⁵n⁴+30m⁴n⁴

300

5w(-7w+3)-2(13-9w²)

18w³-35w²-11w

400

-2r(r³-6r²+6)+4r³-(5r⁴+10r)

-7r⁴+16r³-22r

500

4b[2a²-5(3ab-2b²)]+29ab²

8a²b-31ab+4ab³

Vocabulary

100

Whats a polynomial?

an equation that contains variables and constants, only involving in addition, subtraction, and multiplication.

200

To raise a monomial to a power, use the ____

power rule

300

To multiply monomials, use the ___

Product rule

400

negative exponents can be rewritten using positive exponents using the  ____

Negative exponent rule

500

this order of distributing is frequently referred to as the "____" method

F.O.I.L