How do I solve this (multiplication of exponents)

Question

I can not find any help to spread the exponent across the brackets

$$\left[-3(-2)^2\right]^{-1}$$

Answer 1

$$\left[-3(-2)^2\right]^{-1} = \dfrac{1}{-3(-1\cdot 2)^2} \;=\; \left(-\dfrac{1}{3\left[(-1)^2\cdot 2^2\right]}\right).$$

Now simplify, using the correct order of operations, some of which I've completed above: take exponents, then multiply within the parentheses, then multiply the two resulting terms in the denominator...

Recall:

$a^{-1} = \dfrac{1}{a}\;\;$ for all real $a$, $a\neq 0$

$(ab)^2 = a^2b^2\;\;$ for all $a, b \in \mathbb{R}$

$\dfrac{1}{-a} = \dfrac{-1}{a} = -\dfrac{1}{a}$

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Tip: the acronym PEMDAS is common to help remember the order in which to perform operations It stands for Parentheses, Exponents, (Multiplication, Division), (Addition, Subtraction), and serves as a reminder for remembering the precedence of operations (order to perform operations): Multiplication and Division have equal precedence, so when they occur together in an expression, apply from left to right. Same applies to Addition/subtraction.