3 min read Jun 17, 2024

Understanding (x^5)^4

In mathematics, when dealing with exponents, we often encounter expressions like (x^5)^4. This might seem confusing at first, but it's actually quite simple to understand.

The Power of a Power Rule

The core concept here is the power of a power rule. This rule states:

(a^m)^n = a^(m*n)

In simpler terms, when you raise a power to another power, you multiply the exponents.

Applying the Rule to (x^5)^4

Let's apply this rule to our expression (x^5)^4:

  • a = x
  • m = 5
  • n = 4

Following the rule, we get:

(x^5)^4 = x^(5*4) = x^20

Therefore, (x^5)^4 simplifies to x^20.

Why This Works

The reason this rule works is because of the definition of exponents. Raising something to a power means multiplying it by itself a certain number of times.

For example, x^5 means x multiplied by itself five times: x * x * x * x * x

When we raise x^5 to the power of 4, we are essentially multiplying x^5 by itself four times:

(x^5)^4 = (x^5) * (x^5) * (x^5) * (x^5)

Expanding this, we get:

(x * x * x * x * x) * (x * x * x * x * x) * (x * x * x * x * x) * (x * x * x * x * x)

This results in x being multiplied by itself twenty times, which is represented by x^20.


The power of a power rule is a fundamental concept in algebra. By understanding this rule, we can simplify complex expressions like (x^5)^4 and express them in a much more concise way.

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