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Power of a Power Property

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Power of a Power Property

Study Guide

Key Definition

To find a power of a power, multiply the exponents: $(a^b)^c = a^{b \times c}$

Important Notes

The power of a power property simplifies expressions with exponents
Multiply the exponents for nested exponents
This property is based on the product of powers property
Use this property to simplify complex expressions
Remember: $(a^b)^c = a^{b \times c}$

Mathematical Notation

$\times$ represents multiplication

$^$ denotes exponentiation

$(a^b)^c = a^{bc}$ is the power of a power property

Remember to use proper notation when solving problems

Why It Works

When you multiply an expression by itself repeatedly, it's equivalent to raising it to a power. This is why $(a^b)^c = a^{b \times c}$.

Remember

Keep the power of a power property in mind: $(a^b)^c = a^{b \times c}$

Quick Reference

Property:$(a^b)^c = a^{b \times c}$

Understanding Power of a Power Property

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

When you raise a power to another power, you multiply the exponents. For example, $(a^b)^c = a^{b \times c}$ because you're repeating multiplication b \times c times.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Simplify $(2^3)^2$

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Alex is building a cube and needs to calculate the volume of a cube with side length $(3^2)^2$ cm.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If $(x^2)^3 = x^n$, what is $n$?

Challenge Quiz

Single Choice Quiz

Advanced

Simplify $\left((a^2)^3\right)^2$

Recap

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