Laws of Exponents

Exponents

100

Identify the base: 3²

What is 3

200

Identify the exponent 1⁶

What is 6.

300

Write using exponents: (3 x 3 x 3)

What is 3³

400

Write in expanded form: 9⁶

What is 9 x 9 x 9 x 9 x 9 x 9

500

Simplify x² if x=-3

What is 9

Product of Powers

100

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

What is add.

200

Simplify: (a²)(a⁶)

What is a⁸

300

Simplify: (2x²)(4x³)

What is 8x⁵

400

Simplify: (8x³)(-3x⁹)(2x⁴)

What is -48x¹⁶

500

(15x²y³)(2x^-5y)

30y⁴/x³

Quotient of Powers

100

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

What is subtract

200

Simplify: m⁵/m²

What is m³

300

Simplify: 16w³/4w⁸

What is 4/w⁵

400

-10a⁷b/15a³b⁵

What is -2a⁴/3b⁴

500

Simplify: 6x^-4y⁹/12x^-3y^-2

What is y¹¹/2x

Power of Powers

100

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

What is multiply

200

Simplify: (z³)⁵

What is z¹⁵

300

Simplify: (2x³)⁴

What is 16x¹²

400

Simplify: (3x⁹y²)⁴

What is 81x³⁶y⁸

500

Simplify: (2x²y^-6)^-3

What is y¹⁸/8x⁶

Negative and Zero Exponents

100

Any number raised to the zero power is

What is 1

200

3x⁰

What is 3

300

What mathematical operation does a negative exponent imply?

What is division.

400

Write using positive exponents: 3w^-3z⁶/y^-5

What is 3y⁵z⁶/w³

500

Write x^-2 using positive exponents.

What is 1/x²