Question

show that (-11/13×9/17)^-9=(13/9×17/-11)^9​

Answer 1

Step-by-step explanation:

We are given,

Show that ((-11/13) × (9/17))^-9 = ((13/9) × (17/-11))^9

Now, before solving, we must know an important results,

a^(-m) = 1/(a^m)

Now,

LHS = ((-11/13) × (9/17))^(-9)

= ((-11) × 9)/(13 × 17))^(-9)

= (-99/221)^(-9)

= (221/(-99))^(-9)

We know that, denominator will not have a -ve sign,

Hence,

LHS = (-221/99)^9

Now,

RHS = ((13/9) × (17/-11))^9

= ((13 × 17)/(9 × -11))^9

= (221/-99)^9

Similarly,

RHS = (-221/99)^9

Thus,

LHS = RHS

∴ ((-11/13) × (9/17))^(-9) = ((13/9) × (17/-11))^9

Hope it helped and you understood it........All the best