Question

{(1/2)^-1-(4/5)^-1}^-3

Answer 1

Step-by-step explanation:

Question :-

$\bigg [( \dfrac{1}{2})^{ - 1} - ( \dfrac{4}{5})^{ - 1} \bigg] ^{ - 3}$

To find :-

Value of the equation

Solution :-

We have to make the power positive, or else we can't solve it by negative sign but some cases we have to do it by negative sign . But in this this sum we have to make power negative first and then solve .Now whenever we remove the power of negative to positive or positive to negative we have to flirt the fraction then only we can do the power opposite. So, let's solve it!!

$\bigg [( \dfrac{2}{1})^{ 1} - ( \dfrac{5}{4})^{ 1} \bigg] ^{ - 3}$

${\tt \leadsto} \bigg[ {2}^{1} - ( \dfrac {5} {4})^{1} \bigg] ^{ - 3}$

${\tt \leadsto} \bigg[ \dfrac{8 - 5}{4} \bigg] ^{ - 3} \rightarrow \bigg[ \dfrac{3}{4} \bigg] ^{ - 3}$

Now, again to remove the negative power we have to flirt it.

${\tt \leadsto} \bigg[\dfrac{4}{3} \bigg] ^{3}$

${\tt \leadsto} \bigg[\dfrac{4 ^{3} }{3 ^{3} } \bigg]$

${\tt \leadsto} \bigg[\dfrac{64 }{27 } \bigg]$

${\tt \leadsto} 2\dfrac{10}{27 }$