Question

Please give me all answers

Answer 1

i ) ( 5 / 9 ) ^ - 2 × ( 3 / 5 ) ^ - 3 × ( 3 / 5 ) ⁰

( 5 / 9 ) ^ - 2 × ( 3 / 5 ) ^ - 3

81 / 25 × ( 3 / 5 ) ^ - 3

81 / 25 × ( 125 / 27 )

15

ii ) ( - 3 / 4 ) ^ - 4 × ( - 2 / 5 ) ²

( - 3 / 4 ) ^ - 4 × ( - 2 / 5 ) ²

256 / 81 × ( - 2 / 5 ) ²

256 / 81 × ( - 2 / 5 ) ²

258 / 81 × ( 4 / 25 )

1024 / 2025

iii ) ( - 2 / 3 ) ^ - 3 × ( - 2 / 3 ) ^ - 2

( - 2 / 5 ) ^ - 5

( - 2/5 ) ^ - 5

- 243/32

Answer 2

Solution - 1

$\sf \bigg( \: \dfrac{5}{9} \: \bigg)^{ - 2} \: \times \: \: \bigg( \: \dfrac{3}{5} \: \bigg)^{ - 3} \: \times \: \bigg( \: \dfrac{3}{5} \: \bigg)^{0}$

$\sf \bigg( \: \dfrac{9}{5} \: \bigg)^{2} \: \times \: \: \bigg( \: \dfrac{5}{3} \: \bigg)^{3} \: \times \: \large1$

$\sf \dfrac{9 \: \times \: 9}{5 \: \times \: 5} \: \: \times \: \: \dfrac{5 \: \times \: 5 \: \times \: 5}{3 \: \times \: 3 \: \times 3} \: \: \times \: \: \large1$

$\sf \dfrac{81}{25} \: \: \times \: \: \dfrac{125}{27} \: \: \times \: \: \large1$

$\sf \: Now, \: We \: will \: do \: the \: cutting.$

$\sf \dfrac{3}{1} \: \: \times \: \: \dfrac{5}{1} \: \: \times \: \: \large1$

$\bf \: So, \: 3 \: \times \: 5 \: = \: 15$

$\sf \blue {So, \: the \: answer \: is \: 15.}$

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Solution - 2

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

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

$\sf \: \dfrac{ - 5 \: \times \: - 5 \: \times \: - 5 \: \times \: - 5}{3 \: \times 3 \: \times \: 3 \: \times 3} \: \: \times \: \: \dfrac{ - 2 \: \times \: - 2}{5 \: \times \: 5}$

$\sf \: \dfrac{ 5 \: \times \: 5 \: \times \: 5 \: \times \: 5}{3 \: \times 3 \: \times \: 3 \: \times 3} \: \: \times \: \: \dfrac{ 2 \: \times \: 2}{5 \: \times \: 5}$

$\sf \dfrac{625}{81} \: \times \: \dfrac{2}{25}$

$\sf \: Now, \: We \: will \: do \: the \: cutting.$

$\sf \dfrac{25}{81} \: \times \: \dfrac{2}{1}$

$\sf \dfrac{25 \: \times \: 2}{81} \: \times \: = \: \dfrac{100}{81}$

$\sf \blue {So, \: the \: answer \: is \: \dfrac{100}{81} }$

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Solution - 3

$\sf \: \bigg( \: \dfrac{ - 2}{3} \: \bigg)^{ - 3} \: \: \times \: \: \bigg( \: \dfrac{ - 2}{3} \: \bigg) ^{ - 2}$

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

$\sf \: \bigg( \: \dfrac{ - 2}{3} \: \bigg) \large^{ \: - \: 3 \: - \: 2}$

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

$\sf \dfrac{ - 2 \: \times \: - 2 \: \times \: \: - 2 \: \times \: - 2 \: \: \times - 2 \: }{3 \: \times \: 3 \: \times \: 3 \: \times \: 3 \: \times \: 3}$

$\sf \longrightarrow \: \dfrac{ - 243}{32}$

$\sf \blue {So, \: the \: answer \: is \: \dfrac{ - 243}{32} }$