Properties of exponents

We will show 8 properties of exponents. Let x and y be a number not equal to zero and let n and m be any integers

Property #1

x⁰ = 1

Example: 4⁰ = 1 and (2500000000000000000000)⁰ = 1

Property #2

xⁿ × x^m = x^{n + m}

Example: 4⁶ × 4⁵ = 4^{6 + 5} = 4¹¹

Property #3

xⁿ ÷ x^m = x^{n − m}

Example: 4⁶ ÷ 4⁵ = 4^{6 − 5} = 4¹

Property #4

(xⁿ)^m = x^{n × m}

(5²)⁴ = 5^{2 × 4} = 5⁸

Property #5

(x × y)ⁿ = xⁿ × yⁿ

(6 × 7)⁵ = 6⁵ × 7⁵

Property #6

x^-n = 1 ÷(xⁿ) = 1/(xⁿ)

8^-4 = 1 ÷ (8⁴) = 1 / (8⁴)

Property #7

(x/y)ⁿ = xⁿ / yⁿ

(8/5)⁴ = 8⁴ / 5⁴

Property #8



Any questions about properties of exponents? Let me know.