Indices

Laws of Indices

100

What are the rules for multiplying or dividing indices?

When multiplying, add the exponents When dividing, subtract the exponents

200

What is the rule for power of zero and power of one?

Any number or variable raised to the power of 0 is equal to 1

Any number or variable raised to the power of 1 is the number itself

300

What are the rules for negative indices?

Find the reciprocal

400

What does the power to power law state?

When a power is raised to another power, multiply the powers to simplify

Law of Multiplying/Dividing

100

Simplify 4⁵ x 4²

4⁷

200

Simplify 2⁴ x 5⁷ x 5³ 

2⁴ x 5¹⁰

300

Simplify 3⁹÷3²

3⁷

400

Simplify 9x⁷y⁵÷3x⁴y³

3x³y²

Zero/One Index

100

Evaluate 2³ x 2⁰

8

200

Evaluate 8¹

8

300

Simplify 4⁰ x 4¹

4 or 4¹

400

Evaluate a⁰ x b⁰ x a²

a²

Negative Indices

100

6^-1

1/6

200

a^-3

1/a³

300

2p^-5

2/p⁵

400

1/q² as a negative power

q^-2

Power to Power

100

(2²)³ = ____

2⁶

200

(x⁵)⁶ = ____ 

x³⁰

300

(a²b)² = _____

a⁴b²

400

(3p²)³ = _____

27p⁶