Question

(12x^6y^3z^10 over 3x^4y^2z^7)^3
Find the coefficient and exponent of x

Answer 1

To simplify the expression \(\left(\frac{12x^6y^3z^{10}}{3x^4y^2z^7}\right)^3\), we first simplify the fraction inside the parentheses:

1. **Divide the coefficients:**
\[
\frac{12}{3} = 4
\]

2. **Divide the powers of \(x\):**
\[
\frac{x^6}{x^4} = x^{6-4} = x^2
\]

3. **Divide the powers of \(y\):**
\[
\frac{y^3}{y^2} = y^{3-2} = y^1 = y
\]

4. **Divide the powers of \(z\):**
\[
\frac{z^{10}}{z^7} = z^{10-7} = z^3
\]

So after simplifying, we have:
\[
\frac{12x^6y^3z^{10}}{3x^4y^2z^7} = 4x^2y z^3
\]

Next, we raise the entire expression to the power of 3:
\[
(4x^2y z^3)^3
\]

Now we apply the exponent to each part:
1. **Coefficient:**
\[
4^3 = 64
\]

2. **Power of \(x\):**
\[
(x^2)^3 = x^{2 \cdot 3} = x^6
\]

3. **Power of \(y\):**
\[
(y)^3 = y^3
\]

4. **Power of \(z\):**
\[
(z^3)^3 = z^{3 \cdot 3} = z^9
\]

Combining all these, we get:
\[
64x^6y^3z^9
\]

### Final Answer
- The coefficient is \(64\).
- The exponent of \(x\) is \(6\).