Question

Simplify [4a^(-6) b^2]^(-3) write your answer using only positive exponent

Answer 1

For this case we must simplify the following expression:

`(4a^( - 6) * b ^ 2)^( - 3)`

By definition of power properties we have:
`a ^ {-1} = \frac {1} {a ^ 1} = \frac {1} {a}`

Then, rewriting the expression:

`(\frac {4} {a ^ 6} * b ^ 2) ^ {- 3} =\\\frac {1} {(\frac {4} {a ^ 6} * b ^ 2)^3} =\\\frac {1} {(\frac {4b ^ 2} {a ^ 6})^3} =`

By definition we have to:

`(a ^ n) ^ m = a ^ {n * m}`

`\frac {1} {\frac {64b ^ 6} {a^(18)}}\\\frac {a^(18)} {64b ^ 6}`

Answer:

`\frac {a^(18)} {64b ^ 6}`