Question

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Answer 1

Step-by-step explanation:

$\frac{4}{ {216}^{ \frac{ - 2}{3} } } + \frac{1}{ {216}^{ \frac{ - 3}{4} } } + \frac{2}{ {243}^{ \frac{ - 1}{5} } } \\ =( 4 \times {216}^{ \frac{2}{3} } ) + ( {216}^{ \frac{3}{4} } ) + (2 \times {243}^{ \frac{1}{5} } ) \\ = (4 \times \sqrt[3]{ {(216)}^{2} } ) + ( \sqrt[4]{ {216}^{3} } )+ (2 \times \sqrt[5]{243} ) \\ = (4 \times \sqrt[3]{216 \times 216} ) + ( \sqrt[4]{216 \times 216 \times 216} ) + (2 \times \sqrt[5]{243} ) \\ = (4 \sqrt[3]{ {2}^{3} \times {3}^{3} \times {2}^{3} \times {3}^{3} } ) + ( \sqrt[4]{ {2}^{3} \times {3}^{3} \times{2}^{3} \times {3}^{3} \times{2}^{3} \times {3}^{3} } ) + (2 \times \sqrt[5]{ {3}^{5} } ) \\ = (4 \times 2 \times 2 \times 3 \times 3) + ( \sqrt[4]{ {2}^{4 } \times {3}^{4} \times {2}^{4} \times {3}^{4} \times 2 \times 3 } ) + (2 \times 3) \\ = (144) + (2 \times 2 \times 3 \times 3 \sqrt[4]{6} ) + 6 \\ = 150 + 36 \sqrt[4]{6}$