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Q.20) Show that $\sqrt[3]{27} \times \sqrt[3]{1728} = \sqrt[3]{1728 \times 27}$

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LHS = \sqrt[3]{27} \times \sqrt[3]{1728} = \sqrt[3]{3 \times 3 \times 3} \times \sqrt[3]{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3} = \sqrt[3]{3 \times 3 \times 3} \times \sqrt[3]{12 \times 12 \times 12} = 3 \times 12 = 36 RHS = \sqrt[3]{1728 \times 27} = \sqrt[3]{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3} = 2 \times 2 \times 3 \times 3 = 4 \times 9 = 36 So, LHS = RHS

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