Question

(69 POINTS!!!)

Answer 1

Answer:

3 (x^6 y^4)^(1/3)

Step-by-step explanation:

Answer 2

Answer:

$\boxed{\bold{3x^2y\sqrt[3]{y}}}$

Explanation:

$\bold{\sqrt[3]{27x^6y^4}}$

$\bold{\mathrm{Apply\:radical\:rule\:}\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0}$

$\bold{=\sqrt[3]{27}\sqrt[3]{x^6}\sqrt[3]{y^4}}$

$\bold{\sqrt[3]{27} \ = \ 3}$

$\bol=3\sqrt[3]{x^6}\sqrt[3]{y^4}d$

$\bol\mathrm{Apply\:exponent\:rule}\quad \:a^{bc}=\left(a^b\right)^cd: \ x^6=x^{2\cdot \:3}=\left(x^2\right)^3$

$\bol=3\sqrt[3]{\left(x^2\right)^3}\sqrt[3]{y^4}d$

$\bold{\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\ge 0: \ \sqrt[3]{\left(x^2\right)^3}=x^2}$

$\bold{=3x^2\sqrt[3]{y^4}}$

$\bold{\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c}$

$\bold{=3x^2\sqrt[3]{y^3y^1}}$

$\bold{\mathrm{Apply\:radical\:rule}:\quad \sqrt{a\cdot b}=\sqrt{a}\sqrt{b}}$

$\bold{=3x^2\sqrt[3]{y^3}\sqrt[3]{y^1}}$

$\bold{\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\ge 0: \ \sqrt[3]{y^3}=y}$

$\bold{=3x^2y\sqrt[3]{y^1}}$

$\bold{\mathrm{Apply\:rule}\:a^1=a: \ y^1=y}$

$\boxed{\bold{3x^2y\sqrt[3]{y}}}$

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