Properties of Exponents

Zero/Negative Exponents

100

6⁰

What is 1?

200

1

What is (x)⁰? 

**Any number other than zero could be used for x

300

1/6⁷

What is 6^-7

400

1/64

What is 8^-2

500

(2⁰)(1/6³)

6^-3

Product of a power

100

(3⁴)(3²)

What is 3⁶?

200

5^-3 times 5⁵

What is 5²?

300

(x⁴)(x⁵) 

What is x⁹?

400

4z⁵ times 5z⁴

What is 20z⁹?

500

14x⁸

What is 2x^a times 7x^b?

*where a+b = 8

Quotient of a power

100

8⁹/8⁴

What is 8⁵?

200

3⁵/3⁷

What is 3^-2? 

What is 1/3²

300

y⁷/y²

What is y⁵?

400

9x⁴/3x²

What is 3x²?

500

z⁹

What is z^a/z^b?

*where a-b = 9

Power of a power/product

100

(3⁶)⁸

What is 3⁴⁸

200

(x⁵)⁹

What is x⁴⁵

300

(3x)²

What is 3² times x²?

400

(5²)³ times (5x)⁶

What is (5⁶)(5⁶)(x⁶) ?

What is 5¹²x⁶?

500

(7x⁵y²z⁶)⁴

What is 7⁴x²⁰y⁸z²⁴?

Rules of Exponents

100

Negative Exponents Rule

What is a^-b = 1/a^b

200

Product of Powers Rule

What is a^m times aⁿ = a^m+n?

300

Quotient of powers rule

What is a^m/aⁿ = a^m-n?

400

Power of a power rule

What is (a^c)^d = a^cd?

500

Power of a product rule

What is (ab)^m= a^m times b^m?