Question
Evaluate: $\Big[5\Big(8^{\frac{1}{3}}+27^{\frac{1}{3}}\Big)^3\Big]^{\frac{1}{4}}$
✓
Answer
$\Big[5\Big(8^{\frac{1}{3}}+27^{\frac{1}{3}}\Big)^3\Big]^{\frac{1}{4}}$
$=\Big[5\Big(2^{3\times\frac{1}{3}}+3^{3\times\frac{1}{3}}\Big)^3\Big]^{\frac{1}{4}}$
$=\big[5(2+3)^3\big]^{\frac{1}{4}}$
$=\big[5(5)^3\big]^{\frac{1}{4}}$
$=\big[5^4\big]^{\frac{1}{4}}$
$=5$
$=\Big[5\Big(2^{3\times\frac{1}{3}}+3^{3\times\frac{1}{3}}\Big)^3\Big]^{\frac{1}{4}}$
$=\big[5(2+3)^3\big]^{\frac{1}{4}}$
$=\big[5(5)^3\big]^{\frac{1}{4}}$
$=\big[5^4\big]^{\frac{1}{4}}$
$=5$
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