Laws of Exponents

Laws of Exponents

Product of Powers

• When multiplying two or more exponential expressions with the same base, add the exponents:
  • a^m × a^n = a^(m + n)
• Example: 2^3 × 2^4 = 2^(3 + 4) = 2^7

Power of a Product

• When raising a product to a power, raise each factor to that power:
  • (ab)^m = a^m × b^m
• Example: (2 × 3)^2 = 2^2 × 3^2 = 4 × 9 = 36

Quotient of Powers

• When dividing two exponential expressions with the same base, subtract the exponents:
  • a^m ÷ a^n = a^(m - n)
• Example: 2^5 ÷ 2^3 = 2^(5 - 3) = 2^2

Power of a Power

• When raising an exponential expression to a power, multiply the exponents:
  • (a^m)^n = a^(m × n)
• Example: (2^3)^2 = 2^(3 × 2) = 2^6

Zero Exponent Rule

• Any nonzero number raised to the power of 0 is equal to 1:
  • a^0 = 1 (where a ≠ 0)
• Example: 2^0 = 1

Laws of Exponents

Product of Powers

• Multiplying exponential expressions with the same base involves adding the exponents.
• Formula: a^m × a^n = a^(m + n)
• Example: 2^3 × 2^4 = 2^(3 + 4) = 2^7

Power of a Product

• Raising a product to a power involves raising each factor to that power.
• Formula: (ab)^m = a^m × b^m
• Example: (2 × 3)^2 = 2^2 × 3^2 = 4 × 9 = 36

Quotient of Powers

• Dividing exponential expressions with the same base involves subtracting the exponents.
• Formula: a^m ÷ a^n = a^(m - n)
• Example: 2^5 ÷ 2^3 = 2^(5 - 3) = 2^2

Power of a Power

• Raising an exponential expression to a power involves multiplying the exponents.
• Formula: (a^m)^n = a^(m × n)
• Example: (2^3)^2 = 2^(3 × 2) = 2^6

Zero Exponent Rule

• Any nonzero number raised to the power of 0 is equal to 1.
• Formula: a^0 = 1 (where a ≠ 0)
• Example: 2^0 = 1