Rewrite the rational exponent as a radical by extending the properties of integer exponents.

2 to the 3 over 4 power, all over 2 to the 1 over 2 power

2^(3/4)

----------- = 2^(3/4 - 1/2) = 2^(1/4)
2^(1/2)

To rewrite the rational exponent as a radical, we can use the properties of integer exponents.

First, let's rewrite the rational exponent using the property that (a^m)^n = a^(m*n).

2^(3/4) can be written as (2^3)^(1/4).

Applying the property, we get (2^3)^(1/4) = 2^(3*(1/4)) = 2^(3/4).

Now, let's rewrite the expression with the radical symbol.

2^(3/4) is equivalent to the fourth root of 2^3.

So, the rewritten expression is ∛(2^3), which means the cube root of 2^3.

To rewrite the rational exponent as a radical, we can use the properties of integer exponents.

First, let's consider the numerator: 2 raised to the power of 3/4. We can rewrite this as the fourth root of 2 cubed (since the denominator of the exponent is 4). So, the numerator becomes the fourth root of 2^3, which can be written as ∛(2^3).

Next, let's look at the denominator: 2 raised to the power of 1/2. We can rewrite this as the square root of 2 (since the denominator of the exponent is 2). So, the denominator becomes the square root of 2, which can be written as √2.

Now, combining both the numerator and the denominator, we have (∛(2^3)) / (√2). This is the desired expression with the rational exponent rewritten as a radical using the extended properties of integer exponents.