(16x^4)^1/4

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (16x^4)^1/4

In mathematics, simplifying expressions is a key skill. Let's break down how to simplify the expression (16x^4)^1/4.

Understanding Exponents and Fractional Exponents

• Exponents: An exponent indicates how many times a base number is multiplied by itself. For example, 2^3 means 2 * 2 * 2 = 8.
• Fractional Exponents: A fractional exponent represents a root. The denominator of the fraction indicates the type of root. For example, x^(1/2) means the square root of x.

Applying the Rules

To simplify (16x^4)^1/4, we use the following rules:

1. Power of a Product: (ab)^n = a^n * b^n
2. Power of a Power: (a^m)^n = a^(m*n)

Step-by-Step Simplification

1. Apply the Power of a Product rule: (16x^4)^1/4 = 16^(1/4) * (x^4)^(1/4)
2. Apply the Power of a Power rule: 16^(1/4) * (x^4)^(1/4) = 16^(1/4) * x^(4 * (1/4))
3. Simplify: 16^(1/4) * x^(4 * (1/4)) = 16^(1/4) * x^1
4. Evaluate the root: 16^(1/4) = 2 (since 222*2 = 16)
5. Final Result: 2 * x^1 = 2x

Conclusion

Therefore, the simplified form of (16x^4)^1/4 is 2x. This demonstrates how understanding the rules of exponents and fractional exponents allows us to effectively simplify complex expressions.