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