Question

Simplify the expression express the filial result without using zero or negative integers as exponents (ab^3c^2)^-6

Answer 1

Recall that, if a and b are real numbers different from zero, and m and n are integers then:

`\begin{gathered} (a^{}b)^m=a^mb^m, \\ (a^n)^m=a^(nm), \\ a^(-m)=(1)/(a^m). \end{gathered}`

Using the above properties of exponents we get that:

`(ab^3c^2)^(-6)=(1)/((ab^3c^2)^6)=(1)/(a^6b^(18)c^(12))\text{.}`

Answer:

`(1)/(a^6b^(18)c^(12))\text{.}`