Question

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

Answer 1

Answer:

The solution for the given expression is $x^{38}$ , i.e option C

Step-by-step explanation:

Given expression as :

$(\dfrac{x^{6}\times x^{10}}{x^{-3}})^{2}$

Now, From the common radix method

∵ In multiplication of radix , if the radix is same , then power is added

I.e $x^{6}\times x^{10$ = $x^{6+10}$

Or , $x^{6}\times x^{10$ = $x^{16}$

Now, The expression can be written as

$(\frac{x^{16}}{x^{-3}})^{2}$

And In Division of radix , if the radix is same , then power is subtracted

So, $\frac{x^{16}}{x^{-3}}$

Or, $x^{16 - (-)3}$

Or,  $x^{16 + 3}$

or, $x^{19}$

∴ The expression is now

$(x^{19})$²

Now, again this is written as

$x^{19}$ × $x^{19}$

I.e here again the radix is same and in multiple for, so, power is added

∴ $x^{19}$ × $x^{19}$  = $x^{19+19}$

I.e $x^{19}$ × $x^{19}$ =  $x^{38}$

Hence The solution for the given expression is $x^{38}$ , i.e option C  . Answer