Consider the expression. (x^3y^-2/2^2x^-5y^3)^3. What is the result of applying the quotient of powers rule to the expression?

Answer:[tex]\frac{x^{24} }{8y^{15}}[/tex]Step-by-step explanation:[tex](\frac{x^{3}y^{-2}}{2x^{-5}y^{3}})^3[/tex]We will use 1)Product Rulea^m ∙ a^n = a^(m + n), this says that to multiply two exponents with the same base, you keep the base and add the powers. 2)Quotient Rule[tex]\frac{a^{m} }{a^{n}}=a^{m-n}[/tex]this says that to divide two exponents with the same base, you keep the base and subtract the powers.So by considering these two laws[tex](x^{3-(-5)}y^{-2-3}})/2 )^{3}[/tex][tex](\frac{x^{8}y^{-5} }{2})^{3}[/tex][tex](\frac{x^{8} }{2y^{5}})^{3}[/tex]3)Power Rule (Powers to Powers) (a^m)^n = a^(mn)  [tex]\frac{x^{24} }{8y^{15}}[/tex]