Question

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

Answer 1

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

Answer 2

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