(2y^2)^4

Jasonbradley

2 min read

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Jun 16, 2024

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Simplifying (2y^2)^4

In mathematics, simplifying expressions is a crucial skill. Let's break down how to simplify the expression (2y^2)^4.

Understanding the Properties

This expression involves two key properties:

1. Exponents: An exponent indicates repeated multiplication. For example, x^n means multiplying x by itself n times.
2. Power of a Product: This property states that the power of a product is equal to the product of the powers of each factor. In mathematical terms: (ab)^n = a^n * b^n

Simplifying the Expression

Let's apply these properties to simplify (2y^2)^4:

1. Apply the Power of a Product Property: (2y^2)^4 = 2^4 * (y^2)^4

2. Simplify the exponents: 2^4 = 16 and (y^2)^4 = y^(2*4) = y^8

3. Combine the results: 16 * y^8 = 16y^8

Conclusion

Therefore, the simplified form of (2y^2)^4 is 16y^8. By applying the properties of exponents, we can efficiently simplify complex expressions and understand their meaning.