Question

Mark the correct alternative in the following question:

$$\begin{gathered} {\left({25}^2-{15}^2\right)}^{\frac{3}{2}}= \\ \left(\mathrm{a}\right)4000\left(\mathrm{b}\right)8000\left(\mathrm{c}\right)3125\left(\mathrm{d}\right)1024 \end{gathered}$$

Answer 1

Since,

$$\begin{gathered} {\left({25}^2-{15}^2\right)}^{\frac{3}{2}} \\ ={\left(625-225\right)}^{\frac{3}{2}} \\ ={\left(400\right)}^{\frac{3}{2}} \\ ={\left({20}^2\right)}^{\frac{3}{2}} \\ ={20}^{2\times \frac{3}{2}}\left[\mathrm{As},{\left(x^m\right)}^n=x^{mn}\right] \\ ={20}^3 \\ =8000 \end{gathered}$$

Hence, the correct alternative is option (b).