(5xy 2 ) 4

Jasonbradley

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Jun 16, 2024

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Simplifying (5xy^2)^4

In mathematics, simplifying expressions often involves applying the rules of exponents. One such rule states that when raising a product to a power, we raise each factor to that power. Let's break down the simplification of (5xy^2)^4.

Applying the Rule

• (5xy^2)^4 = 5^4 * x^4 * (y^2)^4

Here, we've raised each factor (5, x, and y^2) to the power of 4.

Simplifying Further

• 5^4 * x^4 * (y^2)^4 = 625x^4y^8

We've simplified 5^4 to 625 and applied another rule of exponents: (a^m)^n = a^(m*n). This gives us (y^2)^4 = y^(2*4) = y^8.

The Final Answer

Therefore, the simplified form of (5xy^2)^4 is 625x^4y^8.