Question

by what number should( -2/3)^-3
be divided so that the quotient may (4/27)^-2

Answer 1

Hi ,

Let x should divide ( - 2/3 )^-3 to get

the quotient ( 4/27 )^-2

( -2/3 )^-3 / x = ( 4/27 )^-2

( 3/2 )³ = ( 27/4 )² × x

[ Since ( a/b )^-n = ( b/a )ⁿ]


27/8 × ( 4/27 )² = x

( 27 × 4 × 4 )/( 8 × 27 × 27 ) = x

After cancellation ,

2/27 = x

Therefore ,

Required number = x = 2/27

I hope this helps you.

: )

Answer 2

Answer:

Hi ,

Let x should divide ( - 2/3 )^-3 to get

the quotient ( 4/27 )^-2

( -2/3 )^-3 / x = ( 4/27 )^-2

( 3/2 )³ = ( 27/4 )² × x

[ Since ( a/b )^-n = ( b/a )ⁿ]

27/8 × ( 4/27 )² = x

( 27 × 4 × 4 )/( 8 × 27 × 27 ) = x

After cancellation ,

2/27 = x

Therefore ,

Required number = x = 2/27

I hope this helps you.

Step-by-step explanation: