Power of a Power Property

Definition

The Power of a Power Property is a rule in exponents that states:

This means that when you raise a power to another power, you multiply the exponents.

Explanation:

• a is the base.

• m and n are the exponents.

So, when you have an expression like (a^m)^n, instead of multiplying out the powers, you simply multiply the exponents m and n together to get the new exponent.

Example 1:

(2^3)^4 = 2^3•4 = 2^12 = 4096

Example 2:

(x^2)^5 = x^2•5 = x^10

This rule helps simplify expressions with nested exponents and is useful for solving more complex problems involving exponents.

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