Answer
The given statement is false.
The correct statement is:
$(3x^2)^{-1}=\dfrac{1}{3x^2}$
Work Step by Step
RECALL:
(1) $a^{-m} = \dfrac{1}{a^m}$
(2) $\dfrac{a^m}{a^n} = a^{m-n}$
(3) $a^1=a$
Use the rule (1) above to obtain:
$(3x^2)^{-1} = \dfrac{1}{(3x^2)^1}$
Use rule (3) above to obtain:
$=\dfrac{1}{3x^2}$
Thus, the given statement is false.
The correct statement is: $(3x^2)^{-1}=\dfrac{1}{3x^2}$
