Question

4x^2y^5 times 3x^4y^2 divided by 3x^2y^2 simplify using algebra 1 exponential rules

Answer 1

To simplify the expression \( \frac{4x^2y^5 \times 3x^4y^2}{3x^2y^2} \), we can follow these steps using algebraic rules for exponents:

1. **Multiply the numerators:**
\[
4x^2y^5 \times 3x^4y^2 = (4 \times 3)(x^2 \times x^4)(y^5 \times y^2) = 12x^{2+4}y^{5+2} = 12x^6y^7
\]

2. **Combine with the denominator:**
\[
\frac{12x^6y^7}{3x^2y^2}
\]

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

4. **Apply the quotient rule for exponents:**
- For \(x\):
\[
\frac{x^6}{x^2} = x^{6-2} = x^4
\]
- For \(y\):
\[
\frac{y^7}{y^2} = y^{7-2} = y^5
\]

5. **Combine everything together:**
\[
4x^4y^5
\]

Thus, the simplified expression is:
\[
\boxed{4x^4y^5}
\]