Laws of Exponents

There are many different laws of exponents. This page covers the 3 most frequently studied formulas in Algebra I. If you are looking for other laws, visit our exponents home page.

Video on the Laws of Exponents

Rules and Laws Covered on This Page

• :
  • Example:
    
• Division:
  • Example:
    
• Exponent to an exponent:
  • Example:
    

	What if the base is different?
	Answer:

Problem 1) Simplify $ x^3 \times x^2 $

Answer

Since we are multiplying exponents we add the exponents:

$ x^3 \times x^2 = x^{3+2} = x^5 $

Problem 2) Simplify $ (x^3) ^2 $

Answer

Use the power rule of exponents and multiply exponents:

$ (x^3) ^2 = x^{(3 \times 2)}= x^6 $

Problem 3) Evaluate : $ \frac {x^5}{ x^3} $

Answer

Use the quotient rule of exponents and subtract the exponents:

$ \frac {x^5}{ x^3} = x^{(5 - 3)}= x^2 $

Problem 4) Simplify $ x^{11} \times x^5 $

Answer

Since we are multiplying exponents we add the exponents

$ x^{11} \times x^5 = x^{11+5} = x^{16} $

Problem 5) Simplify $ x^8 \times y^5 $

Answer

You cannot simplify this expression! Remember that all of the rules on this page only work when the exponents have the same base!

Rules and Laws Covered elsewhere

• Negative Exponents:
  • Negative exponents are explained separately here.
• Fraction Exponents
• Fraction exponents are explained separately here