## What Are Exponents? An **exponent** is a shorthand way of writing repeated multiplication of the same number. In electrical math, exponents are often used when dealing with: - **Powers of ten** (scientific notation) - **Voltage and current powers** (Watts = V²/R) - **Units** (e.g., mm², cm³) - **Exponential growth or decay** in signal strength or capacitor charge/discharge ### Exponent Basics An exponent tells you **how many times to multiply the base by itself**. **Format:** $ a^n $ - **a** is the base - **n** is the exponent (or power) This means: $ a^n = a \times a \times a \times \ldots \text{(n times)} $ ### Examples - $2^3 = 2 \times 2 \times 2 = 8$ - $10^4 = 10,000$ - $5^1 = 5$ - $7^0 = 1$ > Any nonzero number raised to the **zero** power is **1**. ### Powers of Ten This is extremely common in electrical work and scientific notation: |Exponent|Value|Example| |---|---|---| |$10^3$|1,000|1 kilovolt (kV)| |$10^6$|1,000,000|1 megohm (MΩ)| |$10^−3$|0.001|1 millivolt (mV)| |$10^−6$|0.000001|1 microamp (μA)| ### Common Electrical Examples #### Ohm’s Law Power Formula: $ P = V^2 \div R $ If $V = 120$ and $R = 60$: $ P = \frac{120^2}{60} = \frac{14400}{60} = 240\ \text{W} $ You square the voltage — an exponent is used in the formula. #### Scientific Notation: Instead of writing 0.000001 A, we write: $ 1 \times 10^{-6}\ \text{A} = 1\ \mu\text{A} $ Instead of writing 4700000 Ω, we write: $ 4.7 \times 10^6\ \Omega = 4.7\ \text{M}\Omega $ ## Summary - Exponents show repeated multiplication - $a^n$ means multiplying a number by itself _n_ times - Exponents of 10 are essential in scientific notation - You will see exponents in formulas, unit prefixes, and test readings