Let's solve each part of the expressions shown in the image step by step.

Expression 1:

$\left(\frac{1}{4} \times \frac{4}{1} - \frac{7}{8}\right)$

1. Multiply $\frac{1}{4}$ by $\frac{4}{1}$: $\frac{1}{4} \times \frac{4}{1} = 1$
2. Subtract $\frac{7}{8}$ from 1: $1 - \frac{7}{8} = \frac{8}{8} - \frac{7}{8} = \frac{1}{8}$

So, the result of the first part is: $\frac{1}{8}$

Expression 2:

$\sqrt[3]{4}$

This is asking for the cube root of 4. Since the cube root of 4 is not an integer, the exact value is: $\sqrt[3]{4} \approx 1.5874$

Expression 3:

$\frac{8}{8} - \frac{7}{8}$ This simplifies to: $\frac{1}{8}$

Expression 4:

$2^3$

This is $2$ raised to the power of $3$: $2^3 = 8$

Expression 5:

$\frac{1}{8} \times \frac{8}{1}$

This simplifies to: $\frac{1}{8} \times 8 = 1$

Final Answer Summary:

1. $\left(\frac{1}{4} \times \frac{4}{1} - \frac{7}{8}\right) = \frac{1}{8}$
2. $\sqrt[3]{4} \approx 1.5874$
3. $\frac{8}{8} - \frac{7}{8} = \frac{1}{8}$
4. $2^3 = 8$
5. $\frac{1}{8} \times \frac{8}{1} = 1$

Would you like any further details or explanations? Here are five related questions to deepen your understanding:

1. How do you simplify fractions with common denominators?
2. What is the cube root of a number and how is it calculated?
3. How do powers of numbers work in arithmetic?
4. Why does multiplying a fraction by its reciprocal result in 1?
5. What is the difference between a square root and a cube root?

Tip: When working with roots and powers, remember that square roots and cube roots are inverses of squaring and cubing, respectively.