Question

find the reciprocal of
​

Answer 1

$\bigg(\dfrac{2}{5}\bigg)^{3} \: \times \: \bigg(\dfrac{5}{4}\bigg)^{2}$

___________ [ GIVEN ]

• We have to find the reciprocal of it.

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→ $\bigg(\dfrac{2}{5}\bigg)^{3} \: \times \: \bigg(\dfrac{5}{4}\bigg)^{2}$

First solve the powers.

→ $\bigg(\dfrac{8}{125}\bigg) \: \times \: \bigg(\dfrac{25}{16}\bigg)$

Now.. Multiply them

→ $\bigg(\dfrac{ { \cancel{8}}^{1} }{125}\bigg) \: \times \: \bigg(\dfrac{25}{ { \cancel{16}}^{2} }\bigg)$

→ $\bigg(\dfrac{ {1} }{125}\bigg) \: \times \: \bigg(\dfrac{25}{{2} }\bigg)$

→ $\bigg(\dfrac{ {1} }{ { \cancel{125}}^{5} }\bigg) \: \times \: \bigg(\dfrac{ { \cancel{25}}^{1} }{{2} }\bigg)$

→ $\bigg(\dfrac{ {1} }{{5} }\bigg) \: \times \: \bigg(\dfrac{{1} }{{2} }\bigg)$

→ $\dfrac{1}{10}$

Now.. take reciprocal of it.

→ 10

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10 is the reciprocal of $\bigg(\frac{2}{5}\bigg)^{3} \: \times \: \bigg(\frac{5}{4}\bigg)^{2}$

__________ [ ANSWER ]

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