Master

Exponent Tables and Patterns

Master exponent tables and patterns with interactive lessons and practice problems! Designed for students like you!

Learn

Get the basics

Practice

Apply your skills

Master

Achieve excellence

Exponent Tables and Patterns

Study Guide

Key Definition

An exponent indicates how many times a number, the base, is multiplied by itself. For example, $2^3$ means $2 \times 2 \times 2$.

Important Notes

The pattern of the ones digit in the powers of 2 is $2, 4, 8, 6$.
The pattern of the ones digit in the powers of 3 is $3, 9, 7, 1$.
The powers of 4 alternate between $4$ and $6$.
Powers of 10 are written as 1 followed by n zeros, where n is the exponent.
The powers of 9 are related to the powers of 3: $9^n = (3^n)^2$.

Mathematical Notation

$+$ represents addition

$-$ represents subtraction

$\times$ represents multiplication

$\div$ represents division

$x^n$ indicates a number x raised to the power of n

Remember to use proper notation when solving problems

Why It Works

By examining the patterns in exponent tables, we can simplify calculations and recognize relationships between different powers such as $2^n$ and $4^n$.

Remember

The exponent tells you how many times to multiply the base by itself, e.g., $3^2 = 3 \times 3$.

Quick Reference

Power of a number:$x^n = x \times x \times \ldots \times x$ (n times)

Understanding Exponent Tables and Patterns

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

An exponent tells us how many times to multiply the base by itself. For example, $2^3$ means $2 \times 2 \times 2 = 8$. In an exponent table for 2, you list $2^1 = 2$, $2^2 = 4$, $2^3 = 8$, and so on.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is $2^3$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You want to buy a game that doubles in price every day. If it starts at $\$2$, how much will it cost after 5 days?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Why do the ones digits of powers of 2 repeat every 4 numbers with the pattern $2, 4, 8, 6$?

Challenge Quiz

Single Choice Quiz

Advanced

What is the result of $(3^2)^3$?

Recap

Watch & Learn

Review key concepts and takeaways