Exponent Rules, because Exponents Rule!

Product and Quotient Rule

100

The Product Rule: x^m * xⁿ = 

x^m+n

200

The Quotient Rule: x^m / xⁿ = 

x^m-n

300

Simplify: x²y * x³y⁴z

x⁵y⁵z

400

Simplify: x²y⁵ / xy³

xy²

500

Simplify: (x²y³ / xy) * (x⁴ / y)

x⁵y

Power Rule

100

The Power Rule: (x^m)ⁿ = 

x^mn

200

Simplify: (z⁵)²

z¹⁰

300

Simplify: (xy)^m

x^myⁿ

400

Simplify: (6x³)²

36x⁶

500

Simplify: (x² / y)⁴

x⁸ / y⁴

Zero and Negative Exponents

100

The Zero Exponent Rule: x⁰ = 

1

200

The Negative Exponent Rule: x^-m = _____ and 1 / x^-m = _____

1 / x^m

x^m

300

Simplify: (7a³b^-1)⁰

1

400

Simplify: -4x⁵y^-2

-4x⁵ / y²

500

Simplify: a^-2b³ / c^-4d^-1

b³c⁴d / a²

Rational Exponents

100

The Rational Exponent Rule: x^m/n = 

The n^th root of x^m (the free version won't let me type math symbols...boo)

200

Re-write in radical form: z^1/3

The 3rd root of z

300

Re-write in radical form: y^3/4

The 4^th root of y³

400

Re-write in exponent form: The 5^th root of z

z^1/5

500

Re-write in exponent form: The 3^rd root of m²

m^2/3

Give me a challenge!

100

The (rectangular prism) fuel tank of my car has the dimensions:

b⁵ by 3c² by 2x³

What is the volume of the fuel tank?

6b⁵c⁵

200

An asteroid travels at a speed of 6⁸ miles per day, how many miles will it travel in 6³ days?

(don't forget units!)

6¹¹ miles

300

The area of a rectangle is 36x⁵y⁷.

The length of the rectangle is 4x²y³.

What is the width of the rectangle?

9x³y⁴

400

The U.S. national debt is about 10¹³ dollars.

If the debt was divided evenly among the roughly 10⁸ adults, how much would each adult owe?

Write your answer as an exponential expression, and then write the actual dollar amount.

10⁵ dollars

$100,000

500

The height of a trapezoid is 4ab³.

The bases of the trapezoid are 2ab and 5ab.

What is the area of the trapezoid?

Hint: A = ¹/₂ (b₁ + b₂) * h

14a²b⁴