Math, asked by yadavpooja82127, 1 year ago

Simplify: (243/32)^-4/5


Mohanchandrabhatt: Hey friend, if you liked the answer please mark the answer as the brillianist answer.
Mohanchandrabhatt: Please mark the answer as the brillianist answer

Answers

Answered by Mohanchandrabhatt
24
Hey freind, your answer is here --

( 243 / 32 ) ^ - 4 / 5
( 3^5 / 2^5 ) ^ - 4 / 5
( ( 3 / 5 ) ^ 5 ) ^ - 4 / 5
using ( ( a ) ^ m ) ^ n ) = a ^ mn
( 3 / 2 ) ^ - 4 / 5 * 5 / 1
( 3 / 2 ) ^ - 4
using ( a ) ^ - m = ( 1 / a ) ^ m
( 2 / 3 ) ^ 4
16 / 81

Hope it helps
Answered by anonymous64
15
Solution ---

( \frac{243}{32})^{ \frac{ - 4}{5} }

Now, we know that 243 = 3^5
and, 32 = 2^5

 = > (\frac{ {3}^{5} }{ {2}^{5} } )^{ \frac{ - 4}{5} }

Using identity -
(a^m / b^m) = (a/b)^m, we get

 = > ( \frac{3}{2} ^{5} ) ^{ \frac{ - 4}{5} }

Using identity -
{(a/b)^m}^ n = (a/b)^ mn, we get

 = > (\frac{3}{2} )^{5 \times \frac{ - 4}{5} }

Cancelling 5 and 1/5, we get

 = > (\frac{3}{2} ) ^{ - 4}

Using identity -
(a/b)^-m = (b/a)^m, we get

 = > ( \frac{2}{3} ) ^{4}

 = > \frac{2 ^{4} }{3 ^{4} }

 = \frac{16}{81}

Hence, that's your answer.

Hope it'll help.. :-D
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