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: \[ \boxed{4x^4y^5} \]