Let's address both questions from the images you've provided.

Question 1: Solve $\sqrt[3]{-64}$

The cube root of a number is the value that, when cubed, gives the original number. In this case, we are dealing with a negative number, and the cube root of a negative number is also negative.

The cube root of $-64$ is calculated as: $\sqrt[3]{-64} = -4$ because $(-4) \times (-4) \times (-4) = -64$.

So the answer is: $\boxed{-4}$

Question 2: Write $\frac{3}{4}x$ as a radical expression

We need to express $x^{\frac{3}{4}}$ in radical form. The general form of converting exponents to radicals is: $x^{\frac{m}{n}} = \sqrt[n]{x^m}$ In this case, $x^{\frac{3}{4}}$ becomes: $x^{\frac{3}{4}} = \sqrt[4]{x^3}$ Thus, the radical form of $x^{\frac{3}{4}}$ is: $\boxed{\sqrt[4]{x^3}}$

Would you like any further explanation on either of these problems?

Here are 5 related questions:

1. How do you compute higher-order roots, such as $\sqrt[5]{-32}$?
2. How do you simplify expressions involving cube roots?
3. Can a cube root of a negative number ever result in a positive value?
4. How do you convert a square root into an exponent?
5. How do fractional exponents behave when multiplied?

Tip: When dealing with fractional exponents, remember that the numerator represents the power, and the denominator represents the root.