Given $ (1.97)^6$

Step 1:

Let $y=x^6$

$dy=6x^5dx$

Step 2:

let $x=2, \Delta x =-0.03$

Then $f(2)=2^6=64$

and $dy=6x^5dx$

$\quad= 6 \times 32 \times (-0.03)$

$\quad=-192 \times 0.03$

$\quad=-5.76$

$\therefore f(1.97)=f(2)+\Delta y$

$\quad=64-5.76$

$\quad=58.24$