Evaluate the expression.

open parentheses fraction numerator 4 over denominator 10 end fraction close parentheses to the power of 3 end exponent

To evaluate the expression:

\[
\left( \frac{4}{10} \right)^3
\]

### Step-by-step solution:

1. Simplify the fraction \(\frac{4}{10}\). 
   \[
   \frac{4}{10} = \frac{2}{5}
   \]

2. Now, raise the simplified fraction to the power of 3:
   \[
   \left( \frac{2}{5} \right)^3 = \frac{2^3}{5^3}
   \]

3. Calculate the powers:
   \[
   2^3 = 8 \quad \text{and} \quad 5^3 = 125
   \]

4. The final expression is:
   \[
   \frac{8}{125}
   \]

Thus, the value of \(\left( \frac{4}{10} \right)^3\) is \(\frac{8}{125}\).

Would you like more details on this, or do you have any other questions?

### Related questions:
1. How do you simplify fractions before exponentiation?
2. What happens if the base of the fraction is negative?
3. How would you handle fractional exponents?
4. What is the result if you raise the denominator to a power of 2 instead?
5. Can this fraction be written as a decimal?

**Tip:** When simplifying fractions, always look for the greatest common divisor (GCD) to reduce them efficiently.

Learn how to simplify and evaluate the expression (4/10)^3 with a detailed, step-by-step solution. This problem covers key math concepts such as simplifying fractions and applying exponentiation. Suitable for students in Grades 6-8.

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