Index Notation: A Step-by-Step Guide for Mastery

This set of vocabulary flashcards covers the fundamental concepts of index notation, including parts of a term, different forms of representation, and geometric interpretations.

Index notation

A shorthand way of writing repeated multiplication to make long math problems look cleaner.

Base Number

The large number at the bottom of a term (e.g., the number $10$ in $10^3$) that is being multiplied.

Index (or Power/Exponent)

The small floating number that tells us how many times to multiply the base by itself.

Index Form

Writing a mathematical expression using a base and an index, such as $3^2$ or $10^4$.

Expanded Form

Writing out the full multiplication of a term, such as $2^5 = 2 \times 2 \times 2 \times 2 \times 2$.

Squared

A specific term used when the index is $2$, representing the area of a square shape ($3^2 = 9$).

Cubed

A specific term used when the index is $3$, representing a 3D cube shape ($2^3 = 8$).

Linear

A term representing one dimension, such as a line, when the power is $1$ ($5^1 = 5$).

Evaluating

The process of calculating the final value of a power by working out the multiplication (e.g., evaluating $2^4$ as $16$).

Power of 10 Trend

The rule stating that the index tells you how many zeros follow the $1$ (e.g., $10^3 = 1000$).