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:

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

Using the above properties of exponents we get that:

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

Answer:

$\frac{1}{a^6b^{18}c^{12}}\text{.}$