simplify this expression showing all work\n$(3x^{4}y)^{2}cdot (2xy^{5})^{3}$
simplify this expression showing all work\n$(3x^{4}y)^{2}cdot (2xy^{5})^{3}$
Answer
Explanation:
Step1: Expand each term using power - of - a - product rule
Use ((ab)^n=a^nb^n) and ((a^m)^n = a^{mn}). For ((3x^{4}y)^{2}), we have (3^{2}(x^{4})^{2}y^{2}=9x^{8}y^{2}). For ((2xy^{5})^{3}), we have (2^{3}x^{3}(y^{5})^{3}=8x^{3}y^{15}).
Step2: Multiply the two expanded terms
Use (a^m\times a^n=a^{m + n}). ((9x^{8}y^{2})\times(8x^{3}y^{15})=(9\times8)x^{8 + 3}y^{2+15})
Step3: Calculate the coefficient and simplify the exponents
(9\times8 = 72), (8 + 3=11), (2+15 = 17).
Answer:
(72x^{11}y^{17})