The image shows a mathematical expression and a multiple-choice question. The expression to evaluate is:

$\frac{16^{\frac{3}{4}} \times \left( \frac{1}{8} \right)^{-1}}{4}$

Let's solve this step-by-step.

Step 1: Simplify the expression $16^{\frac{3}{4}}$

Recall that $16 = 2^4$. So, we have:

$16^{\frac{3}{4}} = (2^4)^{\frac{3}{4}} = 2^{4 \cdot \frac{3}{4}} = 2^3 = 8.$

Step 2: Simplify $\left( \frac{1}{8} \right)^{-1}$

We know that:

$\left( \frac{1}{8} \right)^{-1} = 8.$

Step 3: Multiply the simplified terms

Now, we multiply the simplified results:

$8 \times 8 = 64.$

Step 4: Divide by 4

Now, divide by 4:

$\frac{64}{4} = 16.$

Conclusion

The value of the expression is 16. Thus, the correct answer is:

B. 16

Would you like more details or have any other questions?

Related Questions:

1. How do we handle negative exponents in other expressions?
2. What are some properties of fractional exponents?
3. How do we convert between different forms of exponents?
4. What are the common exponent rules used in solving such expressions?
5. How can you apply logarithms to solve expressions with exponents?

Tip: Always remember that raising a fraction to a negative exponent flips the fraction.