Virginia SOL Math / Algebra I / Expressions & Operations

A.EO.3

Laws of Exponents

What you'll learn

  • Apply the product, quotient, and power rules for exponents
  • Simplify expressions with zero and negative exponents
  • Write answers using only positive exponents

Words to know

Base —
the number or variable being raised to a power
Exponent —
how many times the base is used as a factor
Product rule —
x^a * x^b = x^(a+b)
Quotient rule —
x^a / x^b = x^(a-b)
Power rule —
(x^a)^b = x^(ab)
Zero exponent —
any nonzero base to the 0 power equals 1

Why it matters The laws of exponents keep very large and very small numbers manageable, powering scientific notation and growth models.

Worked examples

Model ItI do

Simplify x^2 * x^3.

The bases are the same, so add the exponents: x^2 * x^3 = x^(2+3) = x^5.

Try It TogetherWe do

Simplify (2x^3)^2.

Raise each factor to the 2nd power: 2^2 * x^(3*2) = 4x^6.

Now YouYou do

Simplify x^7 / x^4 and write the result with a positive exponent.

Same base in a quotient means subtract the exponents. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Simplify: x^2 * x^4.

  2. 2.Simplify: 7^0.

  3. 3.Simplify: y^6 / y^2.

On Level

The core Quick Check from the book.

  1. 1.Simplify: y^4 * y^5.

  2. 2.Simplify: (a^3)^4.

  3. 3.Simplify: 10^0.

  4. 4.Simplify: m^8 / m^3.

  5. 5.Write with a positive exponent: x^(-2).

Challenge

Stretch your thinking.

  1. 1.Simplify: (3x^2)^3.

  2. 2.Simplify and write with a positive exponent: x^3 / x^7.

  3. 3.Simplify: (2a^3 b)^2.