Question

1. $(((-3)^{-3})^{-1}$

Explanation:

Step1: Apply exponent power rule

Use $(a^m)^n = a^{m \times n}$. Here $a=-3$, $m=-3$, $n=-1$:
$$((-3)^{-3})^{-1} = (-3)^{(-3) \times (-1)}$$

Step2: Calculate the exponent

Multiply the exponents:
$$(-3)^{(-3) \times (-1)} = (-3)^3$$

Step3: Evaluate the power

Compute the final value:
$$(-3)^3 = -3 \times -3 \times -3 = -27$$

Answer:

$-27$