What is a simpler form of the radical expression 4 √(1296 x^16 y^12)?

To simplify the radical expression 4 √(1296 x¹⁶ y¹²), we can break it down step by step.

First, let’s look at the term inside the square root, √(1296 x¹⁶ y¹²):

1. Finding the square root of 1296: The number 1296 is a perfect square. Its square root is 36 because 36 × 36 = 1296.
2. Finding the square root of x¹⁶: Since 16 is even, the square root of x¹⁶ is x⁸ (because (x⁸) × (x⁸) = x¹⁶).).
3. Finding the square root of y¹²: Similarly, the square root of y¹² is y⁶ (because (y⁶) × (y⁶) = y¹²).)

Now we can combine these results:

√(1296 x¹⁶ y¹²) = 36 x⁸ y⁶

Next, we multiply this back by 4:

4 × 36 x⁸ y⁶ = 144 x⁸ y⁶

Therefore, the simpler form of the radical expression 4 √(1296 x¹⁶ y¹²) is:

144 x⁸ y⁶