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The problem in the image asks which value is equivalent to \( 256^{\frac{3}{4}} \). Let's solve it:

1. Start by breaking down the expression \( 256^{\frac{3}{4}} \).
   
2. The number 256 can be rewritten as \( 256 = 2^8 \). So, the expression becomes:
   \[
   256^{\frac{3}{4}} = (2^8)^{\frac{3}{4}} = 2^{8 \times \frac{3}{4}} = 2^6
   \]

3. Now, calculate \( 2^6 \):
   \[
   2^6 = 64
   \]

Therefore, the value of \( 256^{\frac{3}{4}} \) is \( 64 \). The correct answer is \( \boxed{64} \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you simplify expressions with fractional exponents?
2. What is the general formula for powers of powers?
3. How do you rewrite numbers as powers of smaller numbers?
4. What other forms can \( 256^{\frac{3}{4}} \) take, using logarithms?
5. Can you solve \( 1024^{\frac{5}{10}} \)?

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

Learn how to simplify and solve the expression 256^(3/4) using properties of fractional exponents. This step-by-step guide shows how to rewrite 256 as a power of 2 and solve for the final value of 64. Suitable for students in Grades 8-10.

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