Question

Find X so that (2/3^-2).......​

Answer 1

as base is same , add the both powers and it's became (2/3)-¹¹=(2/3)²x+¹

now again base is equal than

=-11=2x+1

=2x=-12

=x=-6

Answer 2

${ (\frac{2}{3} )}^{ - 2} \times {(\frac{2}{3} )}^{ - 9} = {(\frac{2}{ 3}) }^{2x + 1} \\ \\ \implies {(\frac{2}{3})}^{ - 2 - 9} = {( \frac{2}{3} )}^{2x + 1} \\ \\ \implies - 11 = 2x + 1 \\ \\ \implies 2x = - 12 \\ \\ \implies \boxed{x = - 6}$

As the bases of both the fractions are equal, hence their power gets add up and at last the base becomes equal in LHS and RHS .

Therefore we can directly make the powers equal. Finally we solved the linear equation .