Laws of Exponents

Exponent Rules

100

When you multiply two exponents together what do you do?

What is add the exponents?

200

When you divide exponents what do you do?

 What is subtract the exponents?

300

When you take an exponent to a power, what do you do with it?

What is multiply it by the exponent?

400

When you have a negative exponent what do you do?

What is put it in the denominator/ or divide the positive exponent by one?

500

What does anything to the zero power equal?

What is 1?

Product Rule

100

(x²)(x³)

x²⁺³    so...      What is x⁵?

200

(x³)(x⁷)

x³⁺⁷  so...       What is x¹⁰ ?

300

(x⁴)(x³y)

x⁴⁺³y so...  x⁷y ?

400

(x⁶y²)(x⁴y³)

x⁶⁺⁴ y²⁺³  so...   What is x¹⁰y⁵ ?

500

(2x⁵y)(2x²y)

(2)(2) = 4    x⁵⁺²  x⁷  y¹⁺¹  so... What is  4x⁷y² ?

Power Rule

100

(x³)³

x⁽³⁾⁽³⁾  so .. What is x⁹ ?

200

(y⁴)⁵

y⁽⁴⁾⁽⁵⁾   so...    What is y²⁰ ?

300

(x³y²)⁴

x⁽³⁾⁽⁴⁾y⁽²⁾⁽⁴⁾ so...    What is x¹²y⁸ ?

400

(x⁴y³z)²

x⁽⁴⁾⁽²⁾y⁽³⁾⁽²⁾z⁽¹⁾⁽²⁾   so .. What is x⁸y⁶z² ?

500

(2x³y²w²)²

2² x⁽³⁾⁽²⁾y⁽²⁾⁽²⁾w⁽²⁾⁽²⁾ so... What is 4x⁶y⁴w⁴?

Quotient Rule

100

a⁴ / a²

a^4-2   so... What is a² ?

200

x²⁰ / x⁵

x^20-5  so... What is x¹⁵ ?

300

x¹²y¹⁰ / x²y⁴

x^12-2 y^10-4   so...  What is x¹⁰y⁶ ?

400

x¹⁴y⁵z⁷ / x²y³z⁵

x^14-2 y^5-3 z^7-5   so...  What is x¹²y²z² ?

500

10x⁸y⁶ / 2x⁴y²

10/2 x^8-4 y^6-2   so... What is 5x⁴y⁴ ?

Negative Rule/Zero Rule

100

x⁰

What is 1 ?

200

x^-9

What is 1/x⁹ ?

300

(x³y⁴)⁰

What is 1?

400

(x^-2)(x^-3)

1/x²⁺³  so  What is 1/x⁵ ?

500

(x^-3y^-2)(x^-7y^-6)

1/x³⁺⁷y²⁺⁶  so... What is 1/x¹⁰y⁸ ?