Question

simplify the expression below

1. \\(\frac{(-2x^3y^4)^3}{(2xy^2)^5}\\)

Explanation:

Step1: Expand numerator via exponent rules

$(-2x^3y^4)^3 = (-2)^3 \cdot (x^3)^3 \cdot (y^4)^3 = -8x^9y^{12}$

Step2: Expand denominator via exponent rules

$(2xy^2)^5 = 2^5 \cdot x^5 \cdot (y^2)^5 = 32x^5y^{10}$

Step3: Divide numerator by denominator

$\frac{-8x^9y^{12}}{32x^5y^{10}} = \frac{-8}{32} \cdot x^{9-5} \cdot y^{12-10}$

Step4: Simplify each term

$\frac{-8}{32} = -\frac{1}{4}$, $x^{9-5}=x^4$, $y^{12-10}=y^2$

Answer:

$-\frac{1}{4}x^4y^2$