Question

by what number should (_3/5)power -3 be divided so that the quotient may be (9/25)power _3

Answer 1

Hi ,

( 3/5 )^-3 / x = ( 9/25 )^-3

[ since ( a/b )^-n = ( b/a )ⁿ ]

( 5/3 )³ = ( 25/9 )³ × x

[( 5/3 )/( 25/9 )]³ = x

[ ( 5 × 9 )/( 3 × 25 ) ]³ = x

( 3/5 )³ = x

Therefore ,

Required number = x = ( 3/5 )³ = 27/125

I hope this helps you.

: )