Question

simplify.
$(-2x^{4}y^{2}z)(-x^{2}yz^{3})^{3}$

Explanation:

Step1: Expand the powered term

Apply power rule: $(a^m b^n c^p)^q = a^{mq} b^{nq} c^{pq}$
$$(-x^2 y z^3)^3 = (-1)^3 (x^2)^3 y^3 (z^3)^3 = -x^{6} y^{3} z^{9}$$

Step2: Multiply the two expressions

Combine coefficients and like variables using $a^m \cdot a^n = a^{m+n}$
$$(-2x^4 y^2 z) \cdot (-x^6 y^3 z^9) = (-2) \times (-1) x^{4+6} y^{2+3} z^{1+9}$$

Step3: Simplify all terms

Calculate coefficients and exponents
$$= 2x^{10} y^{5} z^{10}$$

Answer:

$2x^{10}y^{5}z^{10}$