Section 6.2: Simplifying Expressions with Exponents

Learn to simplify algebraic expressions that include exponents by applying the laws of exponents.

Example 1

Simplify: \( 2^3 \cdot 2^4 \)

Using the product rule: \( a^m \cdot a^n = a^{m+n} \)

\( 2^3 \cdot 2^4 = 2^{3+4} = 2^7 \)

Example 2

Simplify: \( \frac{5^6}{5^2} \)

Using the quotient rule: \( \frac{a^m}{a^n} = a^{m-n} \)

\( \frac{5^6}{5^2} = 5^{6-2} = 5^4 \)

Example 3

Simplify: \( (3^2)^4 \)

Using the power of a power rule: \( (a^m)^n = a^{m\cdot n} \)

\( (3^2)^4 = 3^{2\cdot4} = 3^8 \)

Practice Problems

  1. Simplify: \( 4^5 \cdot 4^2 \)
  2. Simplify: \( \frac{7^8}{7^3} \)
  3. Simplify: \( (2^3)^5 \)
  4. Simplify: \( x^4 \cdot x^0 \)
  5. Simplify: \( \frac{y^0}{y^2} \)