Simplify: 81 4 −8 216 3 +15 32 5 + 225

814−82163+15325+225=344−8633+15255+152 = 3 4× 1 4 −8× 6 3× 1 3 +15× 2 5× 1 5 +15 = 3 1 −8× 6 1 +15× 2 1 +15 =3−48+30+15 =48−48 =0 Therefore, the correct answer is 0.

Simplify: 81 4 −8 216 3 +15 32 5 + 225

814−82163+15325+225=344−8633+15255+152 = 3 4× 1 4 −8× 6 3× 1 3 +15× 2 5× 1 5 +15 = 3 1 −8× 6 1 +15× 2 1 +15 =3−48+30+15 =48−48 =0 Therefore, the correct answer is 0.

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Simplify: $\sqrt[4]{81} - 8 \sqrt[3]{216} + 15 \sqrt[5]{32} + \sqrt{225}$

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answer is D.

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Detailed Solution

$\sqrt[4]{81} - 8 \sqrt[3]{216} + 15 \sqrt[5]{32} + \sqrt{225}$

$= \sqrt[4]{3^{4}} - 8 \sqrt[3]{6^{3}} + 15 \sqrt[5]{2^{5}} + \sqrt{15^{2}}$
$\begin{array}{l} = 3^{4 \times \frac{1}{4}} - 8 \times 6^{3 \times \frac{1}{3}} + 15 \times 2^{5 \times \frac{1}{5}} + 15 \\ = 3^{1} - 8 \times 6^{1} + 15 \times 2^{1} + 15 \\ = 3 - 48 + 30 + 15 \\ = 48 - 48 \\ = 0 \end{array}$
Therefore, the correct answer is 0.