Question

Mark the correct alternative in the following question:

$$\begin{gathered} {\left\{{\left(33\right)}^2-{\left(31\right)}^2\right\}}^{\frac{5}{7}}= \\ \left(\mathrm{a}\right)64\left(\mathrm{b}\right)16\left(\mathrm{c}\right)32\left(\mathrm{d}\right)4 \end{gathered}$$

Answer 1

Since,

$$\begin{gathered} {\left\{{\left(33\right)}^2-{\left(31\right)}^2\right\}}^{\frac{5}{7}} \\ ={\left\{1089-961\right\}}^{\frac{5}{7}} \\ ={\left\{128\right\}}^{\frac{5}{7}} \\ ={\left\{2^7\right\}}^{\frac{5}{7}} \\ =2^{7\times \frac{5}{7}}\left[\mathrm{As},{\left(x^m\right)}^n=x^{mn}\right] \\ =2^5 \\ =32 \end{gathered}$$

Hence, the correct alternative is option (c).