Laws of Exponents

Exponents

100

Identify the base: 3²

 3

200

Identify the exponent 1⁶

6.

300

Write using exponents: (3 x 3 x 3)

What is 3³

400

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

 h⁵

500

Write in expanded form: 9⁶

 9 x 9 x 9 x 9 x 9 x 9

Product of Powers

100

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

 add.

200

Simplify: 5²x 5⁶

5⁸ 

300

Simplify: 2x² times 4x³

 8x⁵

400

Simplify: (8x³)(-3x⁹)

 -24x¹²

500

Simplify (2x )(3x²)(-3x³)

-18x⁶

Quotient of Powers

100

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

 subtract

200

Simplify: 2⁵/2²

 2³ or 8

300

Simplify: w³/w⁸

 1/w⁵

400

18a⁷/6a³

 3a⁴

500

Simplify: 12x²/6x³

 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

  14⁴ or 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