To solve, express both sides with the same base. Since 16 is equal to 2^4, the equation becomes 2^x = 2^4. Thus, the exponents must be equal, making x = 4.

Multiply numerator and denominator by sqrt(7) to rationalize. The numerator becomes 2*sqrt(7) and the denominator becomes 7, creating the fraction 2*sqrt(7) / 7.

Multiply both the top and the bottom by sqrt(5). This produces (5*sqrt(5)) / 5. Dividing by 5 leaves only the term sqrt(5).

Multiply numerator and denominator by sqrt(3) to rationalize. This gives (3*sqrt(3)) / 3. The 3s cancel out, leaving just sqrt(3).

To remove the radical from the denominator, multiply both numerator and denominator by sqrt(2). This results in (1 * sqrt(2)) / (sqrt(2) * sqrt(2)), which simplifies to sqrt(2) / 2.

Using the quotient property, merge the terms into one square root: sqrt(50 / 2). This simplifies to sqrt(25), which has a value of 5.

For division of radicals, divide the radicands (the numbers inside) under a single root. This makes it sqrt(24 / 6) = sqrt(4). The square root of 4 is exactly 2.

Multiplying a square root by itself cancels out the radical, effectively squaring the square root. sqrt(6) * sqrt(6) is sqrt(36), which immediately simplifies to 6.

Use the multiplication property of radicals to combine them into one root: sqrt(2 * 8) = sqrt(16). The square root of 16 perfectly evaluates to 4.

Multiply the numbers inside the roots to get sqrt(100). The principal square root of 100 is 10, completing the simplification.