Laws of Exponents

Exponents

100

Identify the base of 3²

3

200

Identify the exponent of 1⁶

6

300

Write using exponents: (3 x 3 x 3)

3³

400

Write using exponents: 4 x 4 x 4 x h x h x h x h x h

64h⁵

500

Write the expanded form and the value of 6⁴

6x6x6x6 = 1296

Product of Powers

100

If you are multiplying two powers with the same bases, what do you do with their exponents.

Add the exponents

200

Simplify: x¹⁰⁰ (x²¹)

x¹²¹

300

Simplify: 2x² times 4x³

8x⁵

400

Simplify: (8x³)(-3x⁹)

-24x¹²

500

Simplify: (-2x)³ (5x³)

-40x⁶

Quotient of Powers

100

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

Subtract the exponents

200

Simplify: x⁵/x³

x²

300

Simplify: 100x²⁰/-25x⁵

-4x¹⁵

400

-20a⁶b⁸/-2a²b⁷

10a⁴b

500

Simplify: -364m¹⁰n⁹p¹⁷/4m⁹n⁶p⁹

-91mn³p⁸

Power of Powers

100

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

Multiply the exponents

200

Simplify:(z¹¹)⁸

z⁸⁸

300

Give the value of : (4³)²

4096

400

Simplify: (14y)⁴

38416y⁴

500

Simplify: (2x²y³)³

8x⁶y⁹

Negative and Zero Exponents

100

Any number raised to the zero power is

Always 1

200

(200x²y³)⁰

1

300

-12a⁵b⁶c⁴/-2a³b¹⁰c²

6a²c²/b⁴

400

Write using a positive exponent w^-5/x^-10

x¹⁰/w⁵

500

Write w^-2x⁵y^-8z⁷ using positive exponents.

x⁵z⁷/w²y⁸