Question

সরল কর: $\frac{\sqrt[3]{7^2}\cdot\sqrt[3]{7}}{\sqrt7}$

Answer 1

$\frac{\sqrt[3]{7^2}\cdot\sqrt[3]{7}}{\sqrt7}$

$=\frac{7^{2\cdot\frac13}\cdot7^{\frac13}}{7^{\frac12}}$

$=\frac{7^{\frac23}\cdot7^{\frac13}}{7^{\frac12}}$

$=\frac{7^{\frac23+\frac13}}{7^{\frac12}}$

$=7^{\frac23+\frac13-\frac12}$

$=7^{\frac{4+2-3}{6}}$

$=7^{\frac{3}{6}}$

$=7^{\frac12}$

$=\sqrt7$ [Answer]