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Product of Powers Property

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Product of Powers Property

Study Guide

Key Definition

The Product of Powers Property states that when multiplying two exponents with the same base, you add the exponents: $a^m \times a^n = a^{m+n}$

Important Notes

The base must be the same to use the property.
The property applies to any number of terms: $a^m \times a^n \times a^p = a^{m+n+p}$
This property is useful in simplifying expressions.
It is applicable in algebra and calculus.
Understanding this property helps in solving exponential equations.

Mathematical Notation

$+$ represents addition

$-$ represents subtraction

$\times$ represents multiplication

$a^n$ represents a raised to the power of n

Remember to use proper notation when solving problems

Why It Works

The property works because multiplying powers expands to adding the exponents when bases are identical, for example: $(a^m \times a^n) = a^{m+n}$

Remember

Always check that the bases are the same before applying the product of powers rule.

Quick Reference

Property:$a^m \times a^n = a^{m+n}$

Understanding Product of Powers Property

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Simple explanation with $a^m \times a^n = a^{m+n}$

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Simplify $2^3 \times 2^4$

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine you have $3^2$ groups of friends, each group has $3^3$ members. How many friends do you have in total?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Consider the expression $x^4 \times x^5$. What is the simplified form?

Challenge Quiz

Single Choice Quiz

Advanced

Simplify $(a^2)^3 \times a^4$

Recap

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Review key concepts and takeaways