Laws Indices

Reference data and engineering information about laws indices for mathematics applications.

Overview

Engineering reference data for Laws Indices in mathematics.

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Roots of ax² + bx + c = 0.

$c^2 = a^2 + b^2$

Right triangle relationship.

$A = \pi r^2$

Area of a circle.

$\log_b(x) = \frac{\ln(x)}{\ln(b)}$

Change of base formula.

Symbol	Description	Unit
$\pi$	Pi	3.14159...
$e$	Euler's number	2.71828...

Beyond the key formulas, these rules govern how exponents interact during arithmetic operations.

When multiplying terms with the same base, keep the base and add the exponents.

x^y \cdot x^z = x^{(y + z)}

Example: $3^2 \cdot 3^4 = 3^{(2+4)} = 3^6$

When dividing terms with the same base, keep the base and subtract the exponents.

\frac{x^y}{x^z} = x^{(y - z)}

When raising an exponent to another power, keep the base and multiply the exponents.

(x^y)^z = x^{(y \cdot z)}

Example: $(3^2)^4 = 3^{(2 \cdot 4)} = 3^8$

A negative exponent indicates a reciprocal.

x^{-y} = \frac{1}{x^y}

\frac{1}{x^{-y}} = x^y

A fractional exponent represents a root. $x^{y/z}$ is equivalent to the z-th root of $x^y$ .

x^{y/z} = \sqrt[z]{x^y} = (\sqrt[z]{x})^y