Question

simplify \\((4x^{3}y^{15}) \cdot (10x^{6}y^{11})\\). \\(\bigcirc\\ 10x^{9}y^{26}\\) \\(\bigcirc\\ 40x^{18}y^{165}\\) \\(\bigcirc\\ 4x^{18}y^{165}\\) \\(\bigcirc\\ 40x^{9}y^{26}\\)

Explanation:

Step1: Multiply constant coefficients

$4 \times 10 = 40$

Step2: Combine $x$-terms (add exponents)

$x^3 \times x^6 = x^{3+6} = x^9$

Step3: Combine $y$-terms (add exponents)

$y^{15} \times y^{11} = y^{15+11} = y^{26}$

Step4: Combine all simplified terms

$40 \times x^9 \times y^{26}$

Answer:

$40x^9y^{26}$ (matches the fourth option)