which expression is equivalent to $\frac{(x^{6}y^{8})^{3}}{x^{2}y^{2}}$?\n$x^{7}y^{9}$\n$x^{9}y^{12}$\n$x^{12…
which expression is equivalent to $\frac{(x^{6}y^{8})^{3}}{x^{2}y^{2}}$?\n$x^{7}y^{9}$\n$x^{9}y^{12}$\n$x^{12}y^{18}$\n$x^{16}y^{22}$
Answer
Explanation:
Step1: Simplify the numerator using power - of - a - product rule
According to the rule ((ab)^n=a^n b^n), ((x^{6}y^{8})^{3}=x^{6\times3}y^{8\times3}=x^{18}y^{24}).
Step2: Divide by the denominator using quotient rule
The quotient rule states that (\frac{a^m}{a^n}=a^{m - n}). So (\frac{x^{18}y^{24}}{x^{2}y^{2}}=x^{18 - 2}y^{24 - 2}=x^{16}y^{22}).
Answer:
(x^{16}y^{22}) (the last option)