15sqrt8x^16 / 5sqrt2x^4

To simplify the expression (15√8x^16) / (5√2x^4), we can use the properties of exponents and radicals.

First, let's simplify each term individually:
√8 = √(4 * 2) = 2√2 (since √4 = 2)
√2x^16 = (√2)(x^16) = (√2)(x^8 * x^8) = (√2)(x^8) * (√2)(x^8) = 2x^8 (since √2 * √2 = 2)

Similarly,
√2x^4 = (√2)(x^4)

Now, let's substitute these simplified terms back into the expression:
(15√8x^16) / (5√2x^4) = (15 * 2x^8) / (5 * √2x^4)

Now we can cancel out common factors:
(15 * 2x^8) / (5 * √2x^4) = (30x^8) / (√2x^4)

To simplify further, let's combine the terms under the square root:
√(2x^4) = √(2) * √(x^4) = √(2) * x^2 (since √(x^4) = x^2)

Therefore, the final simplified expression is:
(30x^8) / (√2x^4) = (30x^8) / (√2 * x^2)

The x^2 term cancels out, leaving us with:
(30x^6) / √2

So, the simplified expression is (30x^6) / √2.