Polynomials - Exponent Rules Review

Multiplying Monomials

100

Simplify:

(cd²)(c³d²)

c⁴d⁴

200

Simplify:

(4g³h)(-2g⁵)

-8g⁸h

300

Simplify (do not evaluate):

[(4²)²]²

4⁸

400

Simplify:

(2xy)²(-3x²)(4y⁴)

-48x⁴y⁶

500

Simplify:

(2x³y²z²)³(x²z)⁴

8x¹⁷y⁶z¹⁰

Dividing Monomials

100

Simplify:

[(16p⁵q²) / (2p³q³)]⁰

1

200

Simplify:

(x⁴y⁰) / x^-2

x⁶

300

Simplify:

[(-x^-1y)⁰] / [4w^-1y²]

(w) / (4y²)

400

Simplify:

[(2a^-2b)^-3] / [5a²b⁴]

(a⁴) / (40b⁷)

500

Simplify:

[(2x³y²z) / (3x⁴yz^-2)]^-2

(9x²) / (y²z⁶)

Apply the Rules

100

The area of a triangle with a base of 4a²c and height of 6ac³. Show your work.

A = (1/2)(4a²c)(6ac³)

A = 12a³c⁴

200

The volume of a cube with side length, 3h². Show all work for setup and simplifying.

V = (3h²)³

V = 27h⁶

300

The volume of a cylinder with a radius of 3g and a height of 7g². Show all your work from setup to simplifying.

V = (pi)(3g)²(7g²)

V = (pi)(9g²)(7g²)

V = 63(pi)g⁴

400

A panel of four light switches can be set in 2⁴ ways. A panel of five light switches can set in twice this many ways. In how many ways can five light switches be set?

2(2⁴) = 2⁵ = 32 ways

500

Tawa wants to increase her rock collection by a power of three this year and then increase it again by a power of two next year. If she has 2 rocks now, how many rocks will she have after the second year? Show your work.

(2³)² = 2⁶ = 64 rocks

Vocabulary

100

This is the measure from the center to any point equidistant from the center.

Radius

200

This is the amount of space a figure takes up and the type of units that are used to express this value.

Volume and cubic units (units³)

300

This rule says that when dividing powers with the same base, subtract the exponents.

Quotient of Powers (Quotient Rule)

400

This is a number, a variable, or a product of a number and one or more variables.

Monomial

500

For the negative exponent rule, any nonzero number a and any integer n, has a^-n, which is this flipped relation to aⁿ.

Reciprocal

Hodgepodge

100

This is the mathematical term used to describe rate of change.

Slope

200

A right triangle has legs, 9cm and 12cm. What is the length of the missing side?

Hypotenuse is 15cm

(3:4:5 right triangle, scaled by a factor of 3)

300

This value from an equation would describe the flat rate fee on a graph of car rental fees over time.

y-intercept

400

This is point-slope form for a linear equation.

(y - y₁) = m(x - x₁)

500

A geometry preview? This is the vocabulary term used to describe a plane shape (two-dimensional) with straight sides.

Polygon