Fill in the blanks:
(i) $\sqrt[3]{125 \times 27}=3 \times \ldots$
(ii) $\sqrt[3]{8 \times \ldots}=8$
(iii) $\sqrt[3]{1728}=4 \times \ldots$
(iv) $\sqrt[3]{480}=\sqrt[3]{3} \times 2 \times \sqrt[3]{\ldots}$
(v) $\sqrt[3]{\cdots}=\sqrt[3]{7} \times \sqrt[3]{8}$
(vi) $\sqrt[3]{\cdots}=\sqrt[3]{4} \times \sqrt[3]{5} \times \sqrt[3]{6}$
(vii) $\sqrt[3]{\frac{27}{125}}=\frac{\ldots}{5}$
(viii) $\sqrt[3]{\frac{729}{1331}}=\frac{9}{\ldots}$
(ix) $\sqrt[3]{\frac{512}{\ldots}}=\frac{8}{13}$
(i) 5
$\sqrt[3]{125 \times 27}=3 \times \underline{\mathbf{5}}$
$\because \sqrt[3]{125 \times 27}=\sqrt[3]{125} \times \sqrt[3]{27}=\sqrt[3]{5 \times 5 \times 5} \times \sqrt[3]{3 \times 3 \times 3}$
$=5 \times 3$
$=3 \times 5 \quad$ (Commutative law)
(ii) $8 \times 8=64$
$\because \sqrt[3]{8 \times \underline{8 \times 8}}=8$
(iii) 3
$\because \sqrt[3]{1728}=12=4 \times 3$
(iv) 20
$\because \sqrt[3]{480}=\sqrt[3]{\{2 \times 2 \times 2\} \times 2 \times 2 \times 3 \times 5}=2 \times \sqrt[3]{3} \times \sqrt[3]{5 \times 2 \times 2}=\sqrt[3]{3} \times 2 \times \sqrt[3]{20}$
(v) $7 \times 8=56$
$\because \sqrt[3]{7 \times 8}=\sqrt[3]{7} \times \sqrt[3]{8}$
(vi) $4 \times 5 \times 6=120$
$\because \sqrt[3]{4 \times 5 \times 6}=\sqrt[3]{4} \times \sqrt[3]{5} \times \sqrt[3]{6}$
(vii) 3
$\because \sqrt[3]{\frac{27}{125}}=\frac{\sqrt[3]{27}}{\sqrt[3]{125}}=\frac{3}{5}$
(viii) 11
$\because \sqrt[3]{\frac{729}{1331}}=\frac{\sqrt[3]{729}}{\sqrt[3]{1331}}=\frac{9}{11}$
(ix) $13 \times 13 \times 13=2197$
$\because \sqrt[3]{\frac{512}{13^{3}}}=\frac{\sqrt[3]{8^{3}}}{\sqrt[3]{13^{3}}}=\frac{8}{13}$