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Exponents

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Exponents

Study Guide

Key Definition

An exponent refers to the number of times a base is multiplied by itself. For example, $6^2$ means $6 \times 6$.

Important Notes

Exponents represent repeated multiplication. For example, $3^4$ is $3 \times 3 \times 3 \times 3$.
A common mistake is to multiply the base and exponent together instead of raising the base to the power, like $6^2 = 6 \times 6$.
$4^5$ is greater than $5^4$; calculate each to see why.
Exponents with a base of 1 are always 1, such as $1^n = 1$.
When $x^0$ is given, it equals 1, provided $x \neq 0$.

Mathematical Notation

$^$ denotes exponentiation in calculators and computers

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

Remember to use proper notation when solving problems

Why It Works

Exponentiation is a shortcut for repeated multiplication. For example, instead of multiplying $3 \times 3 \times 3 \times 3$, we use $3^4$.

Remember

Exponents simplify expressions and calculations, allowing you to express repeated multiplications succinctly, such as $10^3 = 10 \times 10 \times 10$.

Quick Reference

Square:$x^2$ means $x \times x$

Cube:$x^3$ means $x \times x \times x$

Zero Exponent:$x^0 = 1$ for $x \neq 0$

Understanding Exponents

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Exponents are a way to express repeated multiplication of the same number. For example, $4^2$ is $4 \times 4$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is $5^2$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

If you save $2^4$ dollars each day for 4 days, how much will you have saved in total?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

What is larger: $4^5$ or $5^4$?

Challenge Quiz

Single Choice Quiz

Advanced

Evaluate $(2^3)^2$.

Recap

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Review key concepts and takeaways