Answer:
The solution for the given expression is [tex]x^{38}[/tex] , i.e option C
Step-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 added
I.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 subtracted
So, [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]²
Now, 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
