\sqrt[5]{8^{2}}\cdot\sqrt[4]{16}\cdot\sqrt[3]{2^{5}}

asked by guest
on Apr 06, 2025 at 4:16 pm



You asked:

Evaluate the expression: 825⋅164⋅253\sqrt[5]{{8}^{2}} \cdot \sqrt[4]{16} \cdot \sqrt[3]{{2}^{5}}

MathBot Answer:

825⋅164⋅253=8⋅21315≈14.58755981693146892505768125670652\sqrt[5]{{8}^{2}} \cdot \sqrt[4]{16} \cdot \sqrt[3]{{2}^{5}} = 8 \cdot 2^{\frac{13}{15}} \approx 14.58755981693146892505768125670652

825⋅164⋅253=825⋅164⋅253=645⋅164⋅253=2⋅25⋅164⋅253=2⋅25⋅2⋅253=2⋅25⋅2⋅323=2⋅25⋅2⋅2⋅223=4⋅25⋅2⋅223=8⋅21315\begin{aligned}\sqrt[5]{{8}^{2}} \cdot \sqrt[4]{16} \cdot \sqrt[3]{{2}^{5}}&=\sqrt[5]{8^{2}} \cdot \sqrt[4]{16} \cdot \sqrt[3]{2^{5}}\\&=\sqrt[5]{64} \cdot \sqrt[4]{16} \cdot \sqrt[3]{2^{5}}\\&=2 \cdot \sqrt[5]{2} \cdot \sqrt[4]{16} \cdot \sqrt[3]{2^{5}}\\&=2 \cdot \sqrt[5]{2} \cdot 2 \cdot \sqrt[3]{2^{5}}\\&=2 \cdot \sqrt[5]{2} \cdot 2 \cdot \sqrt[3]{32}\\&=2 \cdot \sqrt[5]{2} \cdot 2 \cdot 2 \cdot 2^{\frac{2}{3}}\\&=4 \cdot \sqrt[5]{2} \cdot 2 \cdot 2^{\frac{2}{3}}\\&=8 \cdot 2^{\frac{13}{15}}\end{aligned}

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