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Quotient of Powers Property

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Quotient of Powers Property

Study Guide

Key Definition

When you divide two powers with the same base, you subtract the exponents. For a real number $a$ ($a \neq 0$) and integer exponents $b$ and $c$, $\frac{a^b}{a^c} = a^{b-c}$.

Important Notes

The base must be the same for the quotient of powers property to apply.
Make sure $a \neq 0$ to avoid division by zero.
Subtract the exponent of the denominator from the exponent of the numerator.
The property helps simplify expressions with exponents.
Always check the base before applying the property.

Mathematical Notation

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

$\frac{a}{b}$ is a fraction

Remember to use proper notation when solving problems

Why It Works

The quotient of powers property works by cancelling out the common factors in the numerator and the denominator, resulting in the subtraction of exponents.

Remember

Always subtract the exponent of the denominator from the exponent of the numerator: $\frac{a^b}{a^c} = a^{b-c}$.

Quick Reference

Property:$\frac{a^b}{a^c} = a^{b-c}$

Understanding Quotient of Powers Property

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Simple explanation with $\frac{a^b}{a^c} = a^{b-c}$

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Simplify $\frac{2^5}{2^3}$

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

If you have $3^7$ candies and you want to divide them among $3^4$ friends, how many candies does each friend get?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

What is the result of $\frac{x^6y^3}{x^2y}$?

Challenge Quiz

Single Choice Quiz

Advanced

Simplify $\frac{(a^3b^2)^4}{(a^2b)^3}$

Recap

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