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

Question

asked May 15, 2020 215k views

1 Answer

Toabi · Answer 1 · 2020-05-21T14:59:16+0000

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:

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