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Algebra Precision
Exponent Calculator (Power & Roots Solver)
Calculate base raised to any power (bx). Supports positive and negative powers, fractional exponents, decimal bases, and scientific notation with full step-by-step exponent laws.
Result: 28
256
Scientific Notation: 2.56e+2
Expanded: 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256
Laws of Exponents & Mathematical Properties
Exponentiation is a mathematical operation involving two numbers: the base $b$ and the exponent or power $x$. It signifies repeated multiplication when $x$ is a positive integer.
Fundamental Laws of Exponents
Product Rule: b^m × b^n = b^(m + n)
Quotient Rule: b^m / b^n = b^(m - n)
Power Rule: (b^m)^n = b^(m × n)
Negative Exponent: b^(-x) = 1 / (b^x)
Fractional Exponent: b^(m/n) = n√(b^m)
Zero Rule: b^0 = 1 (for all b ≠ 0)
Negative & Fractional Exponents
- Negative Exponents: A negative exponent indicates the reciprocal. For instance,
5^(-2) = 1 / (5^2) = 1 / 25 = 0.04. - Fractional Exponents: When an exponent is a fraction $1/n$, it denotes the $n$-th root. For instance,
16^(1/2) = √16 = 4and27^(1/3) = ³√27 = 3.
Frequently Asked Questions
Using the quotient rule: b^n / b^n = b^(n - n) = b^0. Since any non-zero number divided by itself equals 1, b^0 must mathematically equal 1.
If the root (denominator of fraction) is odd, like (-8)^(1/3), the real root is -2. If the denominator is even, like (-4)^(1/2), the result requires complex imaginary numbers (i).
Educational Disclaimer: Local JavaScript math execution uses IEEE-754 double precision standard.