Exponents

Overview

Engineering reference data for Exponents in miscellaneous.

Key Formulas

Unit Conversion

$y = x \cdot k$

Multiply by conversion factor.

Linear Interpolation

$y = y_1 + \frac{(x - x_1)(y_2 - y_1)}{x_2 - x_1}$

Estimate between two known points.

Percentage

$p = \frac{\text{part}}{\text{whole}} \times 100\%$

Part as fraction of whole.

Variables

Symbol	Description	Unit
$x$	Input value	—
$y$	Output value	—
$k$	Conversion factor	—

Fractional Exponents and Properties

$a^{-n} = \frac{1}{a^n}$

$a^{m/n} = (a^m)^{1/n} = (a^{1/n})^m$

$p a^{1/n} \pm q a^{1/n} = (p \pm q) a^{1/n}$

$(a b)^{1/n} = a^{1/n} b^{1/n}$

$\frac{a^{1/n}}{b^{1/n}} = \left(\frac{a}{b}\right)^{1/n}$

$(a^{m x})^{\frac{1}{n x}} = (a^m)^{\frac{1}{n}}$

$(-a)^{1/2} = i a^{1/2}$

where $i$ is the imaginary unit, defined as $i = \sqrt{-1}$.

References

• Original Source