Question

simplify the expression below. \\(dfrac{(16x^{7}y^{-3}z^{2})(xy)}{4x^{8}y^{2}z^{-8}}\\)

Explanation:

Step1: Multiply numerator terms

Multiply coefficients and add exponents of like variables:
$\frac{16x^{7+1}y^{-3+1}z^{2}}{4x^{8}y^{2}z^{-8}} = \frac{16x^{8}y^{-2}z^{2}}{4x^{8}y^{2}z^{-8}}$

Step2: Simplify coefficients

Divide 16 by 4:
$\frac{4x^{8}y^{-2}z^{2}}{x^{8}y^{2}z^{-8}}$

Step3: Simplify $x$-terms

Subtract exponents of $x$:
$4x^{8-8}y^{-2-2}z^{2-(-8)} = 4x^{0}y^{-4}z^{10}$

Step4: Simplify remaining terms

Use $x^0=1$ and rewrite negative exponents:
$4 \cdot 1 \cdot \frac{z^{10}}{y^{4}} = \frac{4z^{10}}{y^{4}}$

Answer:

$\frac{4z^{10}}{y^{4}}$