%5E2%2F48x%5E2y%5E2.jpeg "(-4x^5y)^2/48x^2y^2")
Simplifying the Expression (-4x^5y)^2 / 48x^2y^2
This article will guide you through simplifying the expression (-4x^5y)^2 / 48x^2y^2.
Understanding the Expression
The expression consists of two parts:
- The numerator: (-4x^5y)^2
- The denominator: 48x^2y^2
We will simplify each part separately before combining them.
Simplifying the Numerator
To simplify (-4x^5y)^2, we need to apply the power of a product rule: (ab)^n = a^n * b^n.
Therefore, we have: (-4x^5y)^2 = (-4)^2 * (x^5)^2 * (y)^2
This simplifies to: 16x^10y^2
Simplifying the Denominator
The denominator 48x^2y^2 is already in its simplest form.
Combining the Simplified Parts
Now that we've simplified both the numerator and denominator, we can combine them:
(16x^10y^2) / (48x^2y^2)
To simplify further, we can cancel out common factors. Both the numerator and denominator have factors of 16, x^2, and y^2. Cancelling these out gives us:
x^8 / 3
Final Result
Therefore, the simplified form of the expression (-4x^5y)^2 / 48x^2y^2 is x^8 / 3.