Introduction:

The concept of 'power of powers' in mathematics involves taking a number raised to a power and then raising that result to another power. It's an extension of exponentiation, a fundamental arithmetic operation.



Understanding Power of Powers:



In power of powers, you first calculate the exponentiation of a base number by an exponent, and then raise this result to another exponent.

The operation follows the rule: (a^b)^c = a^(b*c), where a is the base, and b and c are exponents.

Example of Power of Powers:



Consider the expression (2³)²:

First, calculate 2 to the power of 3, which is 2³ = 2 × 2 × 2 = 8.

Then, raise 8 to the power of 2, which is 8² = 8 × 8 = 64.

So, (2³)² equals 64.

Key Points to Remember:



When dealing with power of powers, multiply the exponents.

This rule simplifies the calculation of such expressions.

Practical Applications:



Power of powers is used in advanced mathematical calculations, including algebra, calculus, and in various scientific computations.