Divide :
`36a^(7)` by `-12a^(3)`

Answer

To divide \( 36a^{7} \) by \( -12a^{3} \), we can follow these steps:

### Step 1: Write the expression
We start with the expression:
\[ \frac{36a^{7}}{-12a^{3}} \]

### Step 2: Factor the coefficients
We can factor the coefficients \( 36 \) and \( -12 \):
\[ \frac{36}{-12} \cdot \frac{a^{7}}{a^{3}} \]

### Step 3: Simplify the coefficients
Now, simplify \( \frac{36}{-12} \):
\[ \frac{36}{-12} = -3 \]
So, we have:
\[ -3 \cdot \frac{a^{7}}{a^{3}} \]

### Step 4: Apply the law of exponents
Using the law of exponents \( \frac{a^{m}}{a^{n}} = a^{m-n} \), we can simplify \( \frac{a^{7}}{a^{3}} \):
\[ \frac{a^{7}}{a^{3}} = a^{7-3} = a^{4} \]
Now, we can combine this with the coefficient:
\[ -3 \cdot a^{4} \]

### Step 5: Write the final answer
Thus, the final answer is:
\[ -3a^{4} \]

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