Mathematics, 19.07.2019 18:00 Wethepeeps6048
Express 15 x^1/3y^1/5 using a radical
Answers: 1
![\bf a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\ -------------------------------](/tpl/images/0108/7198/17c78.png)
![\bf \cfrac{15x^{\frac{1}{3}}}{y^{\frac{1}{5}}}\qquad \begin{cases} \frac{1}{3}=\frac{1\cdot 5}{3\cdot 5}\\ \qquad \frac{5}{15}\\\\ \frac{1}{5}=\frac{1\cdot 3}{5\cdot 3}\\ \qquad \frac{3}{15} \end{cases}\implies \cfrac{15x^{\frac{5}{15}}}{y^{\frac{3}{15}}}\implies 15\cdot \cfrac{x^{\frac{5}{15}}}{y^{\frac{3}{15}}}\implies 15\cdot \cfrac{\sqrt[15]{x^5}}{\sqrt[15]{y^3}} \\\\\\ 15\sqrt[15]{\frac{x^5}{y^3}}](/tpl/images/0108/7198/33765.png)
![15\cdot\sqrt[3]{x}\cdot \sqrt[5]{y}](/tpl/images/0108/7198/34ebb.png)
. We are asked to express our given expression using a radical.![a^{\frac{m}{n}}=\sqrt[n]{a^m}](/tpl/images/0108/7198/f8bf3.png)
, we can write terms of our given expression as:![15\cdot\sqrt[3]{x^1}\cdot \sqrt[5]{y^1}](/tpl/images/0108/7198/6d183.png)
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Express 15 x^1/3y^1/5 using a radical...
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