%5E4.jpeg "(x^5)^4")
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.
Conclusion
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.