Question

Which is the simplified form of (2ab/a^-5b^2)^3

Answer 1

Ans: b^3 / 8ab^18

Explanation:

Answer 2

To simplify the given equation we need to review the rules of power:

`(1) \ a^(m) * a^(n) = a^(m+n) \\ (2) \ (a^(m))/(a^(n)) = a^(m-n) \\ (3) \ (a^(m) )^(n) = a^(mn) \\ (4) a^(-m) = (1)/( a^(m) )`

`(5) \ (ab)^(m) = a^(m) * b^(m)`

The given equation is

`( (2ab)/( a^(-5) b^(2) ) )^(3)`
=
`2^(3) * ( (a)/( a^(-5) ) )^3 * ( (b)/( b^(2)) )^3`
=
`8 * ( a^(1-(-5)) )^3 * ( b^(1-2) )^3`
=
`8 * ( a^(6) )^3 * ( b^(-1) )^3`
=
`8 * a^(18) * b^(-3)`
=
`(8a^(18))/( b^(3) )`