Question

1. simplify:

$2x^2y^3 \cdot 4x^3y^6$
$8x^6y^{18}$
$6x^5y^9$
$6x^6y^{18}$
$8x^5y^9$

Explanation:

Step1: Multiply coefficients

Multiply the coefficients 2 and 4: \(2\times4 = 8\)

Step2: Add exponents of \(x\)

For \(x\) terms, use \(a^m\cdot a^n=a^{m + n}\). So \(x^{2}\cdot x^{3}=x^{2 + 3}=x^{5}\)

Step3: Add exponents of \(y\)

For \(y\) terms, use \(a^m\cdot a^n=a^{m + n}\). So \(y^{3}\cdot y^{6}=y^{3+6}=y^{9}\)

Step4: Combine results

Combine the coefficient and the \(x\) and \(y\) terms: \(8x^{5}y^{9}\)

Answer:

\(8x^{5}y^{9}\) (the option with this expression)