Question

1. $(-2x^{3}yz^{-4})(8x^{-5}y^{2}z)$
2. $4cd^{3}·4^{2}c^{-5}d^{2}$

Explanation:

Step1: Multiply coefficients, combine $x$ terms

$(-2 \times 8)x^{3 + (-5)} = -16x^{-2}$

Step2: Combine $y$ terms

$y^{1 + 2} = y^3$

Step3: Combine $z$ terms

$z^{-4 + 1} = z^{-3} = \frac{1}{z^3}$

Step4: Combine all parts (Problem 1)

$-16x^{-2}y^3z^{-3} = \frac{-16y^3}{x^2z^3}$

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Step1: Simplify coefficients, combine $c$ terms

$(4 \times 4^2)c^{1 + (-5)} = (4 \times 16)c^{-4} = 64c^{-4}$

Step2: Combine $d$ terms

$d^{3 + 2} = d^5$

Step3: Combine all parts (Problem 2)

$64c^{-4}d^5 = \frac{64d^5}{c^4}$

Answer:

1. $\frac{-16y^3}{x^2z^3}$
2. $\frac{64d^5}{c^4}$