(x^2)^4 Simplify

2 min read Jun 17, 2024
(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.

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