Learn how exponents compactly represent repeated multiplication, master the laws of exponents, and explore negative and zero powers.
An exponent shows how many times a base number is multiplied by itself. Laws of exponents let us simplify expressions: aᵐ × aⁿ = aᵐ⁺ⁿ, and aᵐ ÷ aⁿ = aᵐ⁻ⁿ.
Express 6×6×6×6 in exponential form.
6⁴
Simplify: 2⁵ × 2³
2⁵⁺³ = 2⁸ = 256
Any nonzero number raised to the power 0 equals 1. A negative exponent means taking the reciprocal: a⁻ⁿ = 1/aⁿ.
Find the value of 5⁰.
1
Simplify: 2⁻³
1/2³ = 1/8
1. Express 5×5×7×7×7 in exponential form.
2. Simplify: 3⁴ ÷ 3²
3. Find the value of 10⁰.
4. Simplify: 4⁻²
5. A sheet of paper is folded in half repeatedly. If its thickness is v, what is the thickness after 5 folds?