Simplify the exponential expression I keep getting this wron

Simplify the exponential expression. I keep getting this wrong so if you could show your work so I can see where I messed up I would be grateful. The / is meaning a dividing sign. Just saying so there is no confusion.

(-6a²b⁸ / 2a⁸ b^-6 )³

Solution

We have (-6a²b⁸ / 2a⁸ b^-6 )³ = (-6/2)³ * ( a² b⁸)³ * ( 1/a⁸b^-6)³ = (-3)³ * (a⁶b²⁴) * ( 1/ a²⁴ b^-18) = -27 *(a⁶b²⁴) * ( a^-24 b¹⁸) = - 27 a^6-24 b²⁴⁺¹⁸ = - 27 a^-18b⁴²

Note: We know that (p^x)^y = p^xy ; p^x * p^y = p^x+y ; and 1/p^x = p^-x . These formulae have been used in simplifying the given expression.