Question

3.) \\((2x^{-2}y^{3})^{3}\\)\
5.) \\(\sqrt{18v^{3}}\\)

Explanation:

Step1: Apply power to each term

$(2x^{-2}y^3)^3 = 2^3 \cdot (x^{-2})^3 \cdot (y^3)^3$

Step2: Calculate each exponent

$2^3=8$, $(x^{-2})^3=x^{-6}$, $(y^3)^3=y^9$

Step3: Rewrite positive exponents only

$8x^{-6}y^9 = \frac{8y^9}{x^6}$
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Step1: Factor radicand into squares

$\sqrt{18v^3} = \sqrt{9 \cdot 2 \cdot v^2 \cdot v}$

Step2: Simplify square roots

$\sqrt{9v^2} \cdot \sqrt{2v} = 3v\sqrt{2v}$

Answer:

1. $\frac{8y^9}{x^6}$
2. $3v\sqrt{2v}$