Simplify: (243/32)^-4/5
Mohanchandrabhatt:
Hey friend, if you liked the answer please mark the answer as the brillianist answer.
Answers
Answered by
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
( 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
15
Solution ---

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

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

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

Cancelling 5 and 1/5, we get

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



Hence, that's your answer.
Hope it'll help.. :-D
Now, we know that 243 = 3^5
and, 32 = 2^5
Using identity -
(a^m / b^m) = (a/b)^m, we get
Using identity -
{(a/b)^m}^ n = (a/b)^ mn, we get
Cancelling 5 and 1/5, we get
Using identity -
(a/b)^-m = (b/a)^m, we get
Hence, that's your answer.
Hope it'll help.. :-D
Similar questions