Question

Evaluate Given Below
$( \frac{1}{2}){}^{ - 2} - ( \frac{1}{3}) {}^{ - 1} + ( \frac{1}{5}) {}^{ - 2}$
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Answer 1

Answer:

20

Step-by-step explanation:

$= ( \frac{1}{2}){}^{ - 2} - ( \frac{1}{3}) {}^{ - 1} + ( \frac{1}{5}) {}^{ - 2} \\ = {(2)}^{2} - {(3)}^{2} + {(5)}^{2}$

$\because \: \frac{m}{n}^{ - a} = \frac{n}{m}^{a}$

Solving further :-

$= 4 - 9 + 25 \\ = 29 - 9 \\ = 20$

Answer 2

Answer:

$\sf \: { \bigg( \dfrac{1}{2}\bigg)}^{ - 2} - { \bigg( \dfrac{1}{3}\bigg)}^{ - 1} + { \bigg( \dfrac{1}{5}\bigg)}^{ - 2}$

$\sf \: = \: {2}^{2} - {3}^{1} + {5}^{2}$

Because

$\boxed{ \sf \: {x}^{ - y} = \frac{1}{ {x}^{ y} } }$

$\sf \: = \: 4 - 3 + 25$

$\sf \: = \: 26$