Laws of Exponents

Exponents

100

Identify the base: 3²

3

200

Identify the exponent 1⁶

6

300

Write using exponents: 3(3)(3)

3³

400

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

h⁵

500

Write in expanded form: 9 ^ 6

9(9)(9)(9)(9)(9)

Product of Powers

100

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

Add

200

Simplify: 5²5⁶

5⁸

300

Simplify: 2x² times 4x³

8x⁵

400

Simplify: (8x³)(-3x⁹)

-24x¹²

500

Make up your own product of powers question.

Varied answers.

Quotient of Powers

100

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

Subtract

200

Simplify: 2⁵/2²

2³

300

Simplify: w³/w⁸

w^-5 or 1/w⁵

400

18a⁷/6a³

3a⁴

500

Simplify: 12x²/6x³

2x^-1 or 2/x

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: (4³)²

4⁶

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 power with a negative exponent, we need to

Get the reciprocal of the base and raise it to a positive exponent

400

Write using a positive exponent w^-5

1/w⁵

500

Write x^-1 using positive exponent.

1/x