Question

(2x^4y^{-2}z^{-5})(3xy^3z^4)^3

Explanation:

Step1: Expand the cubed term

Apply power rule: $(ab^n)^m=a^m b^{n\cdot m}$
$$(3xy^3z^4)^3 = 3^3 x^3 (y^3)^3 (z^4)^3 = 27x^3y^9z^{12}$$

Step2: Multiply the two expressions

Multiply coefficients, add exponents of like bases
$$(2x^4y^{-2}z^{-5})(27x^3y^9z^{12}) = (2\times27)x^{4+3}y^{-2+9}z^{-5+12}$$

Step3: Simplify all terms

Calculate coefficient and exponents
$$= 54x^7y^7z^7$$

Answer:

$54x^7y^7z^7$