The expression you provided is \( \frac{4^a}{10a} \). To simplify this, let's go step by step.

1. **Factor the denominator:**
   The denominator \( 10a \) can be factored as \( 2 \times 5 \times a \).

   So we rewrite the expression as:
   \[
   \frac{4^a}{2 \times 5 \times a}
   \]

2. **Express \( 4^a \) as powers of 2:**
   Since \( 4 = 2^2 \), we can rewrite \( 4^a \) as \( (2^2)^a = 2^{2a} \).

   Now the expression becomes:
   \[
   \frac{2^{2a}}{2 \times 5 \times a}
   \]

3. **Simplify the powers of 2:**
   Using the rules of exponents, \( \frac{2^{2a}}{2} = 2^{2a-1} \).

   Now the expression is:
   \[
   \frac{2^{2a-1}}{5 \times a}
   \]

So, the fully simplified expression is:
\[
\frac{2^{2a-1}}{5a}
\]

### Final Answer:
\[
\frac{2^{2a-1}}{5a}
\]

Would you like more details on any of the steps?

Here are five related questions for further practice:
1. Simplify \( \frac{4^b}{8b} \).
2. Simplify \( \frac{3^{2n}}{9n} \).
3. Simplify \( \frac{6^x}{12x} \).
4. Simplify \( \frac{5^{2m}}{25m} \).
5. Simplify \( \frac{9^k}{3k} \).

**Tip:** When simplifying expressions with exponents, look for common factors in the numerator and denominator to reduce the expression efficiently.

Learn how to fully simplify the algebraic expression ⁴ᵃ⁄₁₀ₐ using exponent rules and fraction simplification. This detailed step-by-step guide demonstrates key algebraic concepts such as expressing powers of 2 and reducing fractions. Ideal for students in Grades 9-11.

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