How to Use Power & Exponent Calculator
- Enter Base ($x$): Enter base value.
- Enter Exponent ($y$): Enter exponent value.
- Click Calculate: See the power product expanded form and scientific notation instantly.
Explanation & How It Works
Exponentiation refers to a mathematical operation where a number, known as the base, is multiplied with itself by the power of an exponent.
Calculation Formula & Rules
x&sup0; = 1 (for any $x \neq 0$)
x¯ⁿ = 1 / xⁿ (negative exponent)
x^(1/n) = ⁿ√x (fractional exponent)
Example Calculation
Example: Calculate 2¯³.
- Apply negative exponent rule:
1 / 2³. - Calculate power:
2 × 2 × 2 = 8. - Result:
1/8 = 0.125.
Exponent Laws Cheat Sheet
- Product Law: $x^a \times x^b = x^{a+b}$
- Quotient Law: $x^a / x^b = x^{a-b}$
- Power of a Power: $(x^a)^b = x^{a \times b}$
Frequently Asked Questions
Why does any number to the power of 0 equal 1?
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Because by the quotient rule, x^n / x^n = x^(n-n) = x^0. Since any non-zero number divided by itself equals 1, x^0 must equal 1.