Algebros - Laws of Exponents

Product of Powers

100

You do this to the exponents to multiply powers with the same base.

add

200

Simplify: v² x v⁶

v⁸

300

Simplify: 2x² times 4x³

8x⁵

400

Simplify: (8x³)(-3x⁹)

-24x¹²

500

-4y²(-3y³z)

12y⁵z

Quotient of Powers

100

You do this to the exponents when dividing powers with the same base.

subtract

200

Simplify: x⁵/x²

x³

300

Simplify: w³/w⁸

w^-5

400

18a⁷/6a³

3a⁴

500

Simplify: 12x^2/6x^3

2x^-1

Power of Powers

100

You do this to the exponents when finding the power to a power.

multiply

200

Simplify: (z¹¹)⁵

z⁵⁵

300

Simplify: (x³)²

 x⁶

400

Simplify: (14y)⁴

38416y⁴

500

Simplify: (x²y⁶)³

 x⁶y¹⁸

Negative and Zero Exponents

100

Any number raised to the zero power is

 1

200

2⁰

1

300

To write a negative fraction using positive exponents, you must make a

fraction

400

Write using a positive exponent w^-5

1/w⁵

500

Write x^-1 using positive exponents.

1/x¹

Multiplying Polynomials

100

Multiply the monomial by the polynomial

5x²(3x+1)

15x³+5x²

200

Multiply Binomials using the FOIL method.

(x-1)(x+4)

x²+3x-4

300

Multiply Binomials using the FOIL method.

(x-5)(-2x+9)

-2x²+19x-45

400

Multiply Bionomials using the FOIL method.

(4x+9y)(3x-7y)

12x²-xy-63y²

500

(2x-1)(5x²+7x+1)

10x³+9x²-5x-1