Which expression is equivalent to (x^6×x^10/×^-3)^2 and why?

Answer: The solution for the given expression is [tex]x^{38}[/tex] , i.e option CStep-by-step explanation:Given expression as :[tex](\dfrac{x^{6}\times x^{10}}{x^{-3}})^{2}[/tex]Now, From the common radix method ∵ In multiplication of radix , if the radix is same , then power is addedI.e [tex]x^{6}\times x^{10[/tex] = [tex]x^{6+10}[/tex]Or , [tex]x^{6}\times x^{10[/tex] = [tex]x^{16}[/tex]Now, The expression can be written as [tex](\frac{x^{16}}{x^{-3}})^{2}[/tex]And In Division of radix , if the radix is same , then power is subtractedSo, [tex]\frac{x^{16}}{x^{-3}}[/tex]Or, [tex]x^{16 - (-)3}[/tex]Or,  [tex]x^{16 + 3}[/tex]or, [tex]x^{19}[/tex]∴ The expression is now [tex](x^{19})[/tex]²Now, again this is written as [tex]x^{19}[/tex] × [tex]x^{19}[/tex]I.e here again the radix is same and in multiple for, so, power is added∴ [tex]x^{19}[/tex] × [tex]x^{19}[/tex]  = [tex]x^{19+19}[/tex]I.e [tex]x^{19}[/tex] × [tex]x^{19}[/tex] =  [tex]x^{38}[/tex]Hence The solution for the given expression is [tex]x^{38}[/tex] , i.e option C  . Answer