Laws of Exponents

Exponential to Radical Form

100

Identify the base: 3^2

What is 3

200

Identify the exponent 1^6

What is 6.

300

Write using exponents: (3 x 3 x 3)

What is 3^3

400

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

What is h^5

500

Write in expanded form: 9 ^ 6

What is 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.

What is add.

200

Simplify: 5^2 x 5^6

What is 5^8

300

Simplify: 2x^2 times 4x^3

What is 8x^5

400

Simplify: (8x^3)(-3x^9)

What is -24x^12

500

3⁷ * 3^y

3⁷⁺⁴

Quotient of Powers

100

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

What is subtract

200

Simplify: 2⁵ / 2²

What is 2³

300

Simplify: w³ / w⁸

What is w^-5 or 1/w⁵

400

18a⁷ / 6a³

What is 3a⁴

500

Simplify: 12x² / 6x³

What is 2x^-1 or 2/x

Power of Powers

100

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

What is multiply

200

Simplify: (z¹¹)⁵

What is z⁵⁵

300

Simplify: (4³)²

What is 4⁶

400

Simplify: (14y)⁴

What is 38416 y⁴

500

Simplify: (x²y⁶)³

What is x⁶y¹⁸

Negative and Zero Exponents

100

Any number raised to the zero power is

What is 1

200

2⁰

What is 1

300

Evaluate 7x⁰

What is 7

400

Write using a positive exponent w^-5

What is 1/w⁵

500

Write a⁶ b⁷c⁴ / a²b⁵c⁶ using positive exponents.

What is a⁴b²/c²