Question Number 43789 by Junaid555 last updated on 15/Sep/18
$$\:{plz}\:{solve}\:{it}\:{for}\:{me}\:{i}\:{am}\:{learning} \\ $$$$ \\ $$$$\:\:\sqrt[{\mathrm{3}}]{\frac{\mathrm{81}}{\mathrm{125}}} \\ $$
Answered by MJS last updated on 15/Sep/18
$$\sqrt[{{n}}]{\frac{{a}}{{b}}}=\frac{\sqrt[{{n}}]{{a}}}{\:\sqrt[{{n}}]{{b}}}\:\:\:\:\:\sqrt[{{n}}]{{a}×{b}}=\sqrt[{{n}}]{{a}}×\sqrt[{{n}}]{{b}} \\ $$$$\sqrt[{{n}}]{{c}^{{n}} }={c} \\ $$$$\mathrm{there}\:\mathrm{are}\:\mathrm{some}\:\mathrm{exceptions}\:\mathrm{but}\:\mathrm{at}\:\mathrm{this}\:\mathrm{level} \\ $$$$\mathrm{it}'\mathrm{s}\:\mathrm{good}\:\mathrm{to}\:\mathrm{remember}\:\mathrm{these} \\ $$$$ \\ $$$$\sqrt[{\mathrm{3}}]{\frac{\mathrm{81}}{\mathrm{125}}}=\frac{\sqrt[{\mathrm{3}}]{\mathrm{81}}}{\:\sqrt[{\mathrm{3}}]{\mathrm{125}}}=\frac{\sqrt[{\mathrm{3}}]{\mathrm{3}×\mathrm{3}×\mathrm{3}×\mathrm{3}}}{\:\sqrt[{\mathrm{3}}]{\mathrm{5}×\mathrm{5}×\mathrm{5}}}=\frac{\sqrt[{\mathrm{3}}]{\mathrm{3}^{\mathrm{3}} ×\mathrm{3}}}{\:\sqrt[{\mathrm{3}}]{\mathrm{5}^{\mathrm{3}} }}= \\ $$$$=\frac{\sqrt[{\mathrm{3}}]{\mathrm{3}^{\mathrm{3}} }×\sqrt[{\mathrm{3}}]{\mathrm{3}}}{\mathrm{5}}=\frac{\mathrm{3}}{\mathrm{5}}\sqrt[{\mathrm{3}}]{\mathrm{3}} \\ $$
Commented by Junaid555 last updated on 15/Sep/18
$${Thank}\:{you}\:{very}\:{much} \\ $$