Divide :
`63a^(4)b^(5)c^(6)` by `-9a^(2)b^(4)c^(3)`

Answer

To divide the expression \( 63a^4b^5c^6 \) by \( -9a^2b^4c^3 \), we can follow these steps:

### Step 1: Separate the constants and variables
We can write the division as:
\[ \frac{63a^4b^5c^6}{-9a^2b^4c^3} = \frac{63}{-9} \cdot \frac{a^4}{a^2} \cdot \frac{b^5}{b^4} \cdot \frac{c^6}{c^3} \]

### Step 2: Divide the constants
Now, we divide the constants:
\[ \frac{63}{-9} = -7 \]

### Step 3: Divide the variables with the same base
Next, we divide the variables:
- For \( a \):
\[ \frac{a^4}{a^2} = a^{4-2} = a^2 \]
- For \( b \):
\[ \frac{b^5}{b^4} = b^{5-4} = b^1 = b \]
- For \( c \):
\[ \frac{c^6}{c^3} = c^{6-3} = c^3 \]

### Step 4: Combine the results
Now, we can combine all the results together:
\[ -7 \cdot a^2 \cdot b \cdot c^3 = -7a^2bc^3 \]

### Final Answer
Thus, the result of dividing \( 63a^4b^5c^6 \) by \( -9a^2b^4c^3 \) is:
\[ -7a^2bc^3 \]

---