%5E4-simplify.jpeg "(x^2)^4 Simplify")
Simplifying (x^2)^4
In mathematics, simplifying expressions is a crucial step in solving equations and understanding mathematical relationships. One common type of simplification involves exponents raised to other exponents. This article will focus on simplifying the expression (x^2)^4.
Understanding the Power of a Power Rule
The key to simplifying this expression lies in understanding the power of a power rule. This rule states that when raising a power to another power, you multiply the exponents. Mathematically, this can be represented as:
(a^m)^n = a^(m*n)
Applying the Rule to (x^2)^4
Let's apply this rule to our expression (x^2)^4.
- a = x
- m = 2
- n = 4
Following the rule, we multiply the exponents:
(x^2)^4 = x^(2*4)
The Simplified Expression
Simplifying further, we get:
(x^2)^4 = x^8
Therefore, the simplified form of (x^2)^4 is x^8.
Conclusion
By applying the power of a power rule, we successfully simplified the expression (x^2)^4 to x^8. Remember, understanding and applying these rules is essential for simplifying complex expressions in various mathematical contexts.