Divide
`28a^(2) " by " 7a^(5)`

Answer

To solve the problem of dividing \( 28a^2 \) by \( 7a^5 \), we will follow these steps:

### Step-by-Step Solution:

1. **Write the Division as a Fraction**:
\[ \frac{28a^2}{7a^5} \]

2. **Separate the Numerical and Variable Parts**:
We can separate the coefficients (numerical parts) and the variables:
\[ \frac{28}{7} \cdot \frac{a^2}{a^5} \]

3. **Divide the Numerical Coefficients**:
Calculate \( \frac{28}{7} \):
\[ 28 \div 7 = 4 \]

4. **Apply the Laws of Exponents to the Variables**:
For the variables, we use the rule \( \frac{a^m}{a^n} = a^{m-n} \):
\[ \frac{a^2}{a^5} = a^{2-5} = a^{-3} \]

5. **Combine the Results**:
Now, we combine the results from the numerical part and the variable part:
\[ 4 \cdot a^{-3} \]

6. **Rewrite the Expression**:
Since \( a^{-3} \) can be rewritten as \( \frac{1}{a^3} \), we have:
\[ 4a^{-3} = \frac{4}{a^3} \]

### Final Answer:
\[ \frac{28a^2}{7a^5} = \frac{4}{a^3} \]

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