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Question Number 43789 by Junaid555 last updated on 15/Sep/18

 plz solve it for me i am learning      (((81)/(125)))^(1/3)

$$\:{plz}\:{solve}\:{it}\:{for}\:{me}\:{i}\:{am}\:{learning} \\ $$$$ \\ $$$$\:\:\sqrt[{\mathrm{3}}]{\frac{\mathrm{81}}{\mathrm{125}}} \\ $$

Answered by MJS last updated on 15/Sep/18

((a/b))^(1/n) =((a)^(1/n) /(b)^(1/n) )     ((a×b))^(1/n) =(a)^(1/n) ×(b)^(1/n)   (c^n )^(1/n) =c  there are some exceptions but at this level  it′s good to remember these    (((81)/(125)))^(1/3) =(((81))^(1/3) /((125))^(1/3) )=(((3×3×3×3))^(1/3) /((5×5×5))^(1/3) )=(((3^3 ×3))^(1/3) /(5^3 )^(1/3) )=  =(((3^3 )^(1/3) ×(3)^(1/3) )/5)=(3/5)(3)^(1/3)

$$\sqrt[{{n}}]{\frac{{a}}{{b}}}=\frac{\sqrt[{{n}}]{{a}}}{\sqrt[{{n}}]{{b}}}\:\:\:\:\:\sqrt[{{n}}]{{a}×{b}}=\sqrt[{{n}}]{{a}}×\sqrt[{{n}}]{{b}} \\ $$$$\sqrt[{{n}}]{{c}^{{n}} }={c} \\ $$$$\mathrm{there}\:\mathrm{are}\:\mathrm{some}\:\mathrm{exceptions}\:\mathrm{but}\:\mathrm{at}\:\mathrm{this}\:\mathrm{level} \\ $$$$\mathrm{it}'\mathrm{s}\:\mathrm{good}\:\mathrm{to}\:\mathrm{remember}\:\mathrm{these} \\ $$$$ \\ $$$$\sqrt[{\mathrm{3}}]{\frac{\mathrm{81}}{\mathrm{125}}}=\frac{\sqrt[{\mathrm{3}}]{\mathrm{81}}}{\sqrt[{\mathrm{3}}]{\mathrm{125}}}=\frac{\sqrt[{\mathrm{3}}]{\mathrm{3}×\mathrm{3}×\mathrm{3}×\mathrm{3}}}{\sqrt[{\mathrm{3}}]{\mathrm{5}×\mathrm{5}×\mathrm{5}}}=\frac{\sqrt[{\mathrm{3}}]{\mathrm{3}^{\mathrm{3}} ×\mathrm{3}}}{\sqrt[{\mathrm{3}}]{\mathrm{5}^{\mathrm{3}} }}= \\ $$$$=\frac{\sqrt[{\mathrm{3}}]{\mathrm{3}^{\mathrm{3}} }×\sqrt[{\mathrm{3}}]{\mathrm{3}}}{\mathrm{5}}=\frac{\mathrm{3}}{\mathrm{5}}\sqrt[{\mathrm{3}}]{\mathrm{3}} \\ $$

Commented by Junaid555 last updated on 15/Sep/18

Thank you very much

$${Thank}\:{you}\:{very}\:{much} \\ $$

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