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navik [9.2K]
3 years ago
13

Which expression is equivalent to ? Assume .

Mathematics
2 answers:
Ymorist [56]3 years ago
8 0

Answer: (x^{\dfrac{2}{7}})(y^{-\dfrac{3}{5}})

Step-by-step explanation:

The given expression : \dfrac{\sqrt[7]{x^2}}{\sqrt[5]{y^3} }

Law of radicals :-

\sqrt[n]{a}=a^{\frac{1}{n}}\\\\\sqrt[n]{a^m}=a^{\frac{m}{n}}

Law of exponent:

\dfrac{1}{a^n}=a^{-n}

Using the above law of radicals and law of exponent we have,

\dfrac{\sqrt[7]{x^2}}{\sqrt[5]{y^3}}\\\\=(x^{\frac{2}{7}})(y^{-\frac{3}{5}})

hichkok12 [17]3 years ago
5 0

\text{Use}\ \sqrt[n]{a^m}=a^{\frac{m}{n}}\ \text{and}\ a^{-1}=\dfac{1}{a}\\\\\dfrac{\sqrt[7]{x^2}}{\sqrt[5]{y^3}}=\left(x^{\frac{2}{7}\right)\left(\dfrac{1}{y^\frac{3}{5}}\right)=\left(x^{\frac{2}{7}}\right)\left(y^{-\frac{3}{5}}\right)

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