Question

Mark the correct alternative in the following question:

$$\begin{gathered} \mathrm{If}abc=0,\mathrm{then}\frac{{\left\{{\left(x^a\right)}^b\right\}}^c}{{\left\{{\left(x^b\right)}^c\right\}}^a}= \\ \left(\mathrm{a}\right)3\left(\mathrm{b}\right)0\left(\mathrm{c}\right)-1\left(\mathrm{d}\right)1 \end{gathered}$$

Answer 1

$$\begin{gathered} \frac{{\left\{{\left(x^a\right)}^b\right\}}^c}{{\left\{{\left(x^b\right)}^c\right\}}^a} \\ =\frac{{\left(x^a\right)}^{bc}}{{\left(x^b\right)}^{ac}}\left[\mathrm{As},{\left(x^m\right)}^n=x^{mn}\right] \\ =\frac{x^{abc}}{x^{abc}}\left[\mathrm{As},{\left(x^m\right)}^n=x^{mn}\right] \\ =\frac{x^0}{x^0}\left[\mathrm{As},abc=0\right] \\ =\frac{1}{1}\left[\mathrm{As},x^0=1\right] \\ =1 \end{gathered}$$