Question

simplify or evaluate the expression \\(\frac{19}{-4z^{-3}}\\)

Explanation:

Step1: Rewrite negative exponent

Recall $z^{-n}=\frac{1}{z^n}$, so $z^{-3}=\frac{1}{z^3}$.
$\frac{19}{-4z^{-3}} = \frac{19}{-4 \cdot \frac{1}{z^3}}$

Step2: Simplify complex fraction

Dividing by a fraction is multiplying by its reciprocal.
$\frac{19}{-4 \cdot \frac{1}{z^3}} = 19 \cdot \frac{z^3}{-4}$

Step3: Rewrite final form

Combine terms to simplify the expression.
$19 \cdot \frac{z^3}{-4} = -\frac{19z^3}{4}$

Answer:

$-\frac{19z^3}{4}$