Question

Express 15 x^1/3y^1/5 using a radical

Answer 1

In short, to convert two fractions to have the same denominator, we simply multiply one by the denominator of the other, so in this case, we'll multiply 1/3 by 5, top and bottom, and 1/5 by 3, top and bottom, thus

$\bf a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\ -------------------------------$

$\bf \cfrac{15x^{\frac{1}{3}}}{y^{\frac{1}{5}}}\qquad \begin{cases} \frac{1}{3}=\frac{1\cdot 5}{3\cdot 5}\\ \qquad \frac{5}{15}\\\\ \frac{1}{5}=\frac{1\cdot 3}{5\cdot 3}\\ \qquad \frac{3}{15} \end{cases}\implies \cfrac{15x^{\frac{5}{15}}}{y^{\frac{3}{15}}}\implies 15\cdot \cfrac{x^{\frac{5}{15}}}{y^{\frac{3}{15}}}\implies 15\cdot \cfrac{\sqrt[15]{x^5}}{\sqrt[15]{y^3}} \\\\\\ 15\sqrt[15]{\frac{x^5}{y^3}}$

Answer 2

Answer:

$15\cdot\sqrt[3]{x}\cdot \sqrt[5]{y}$

Step-by-step explanation:

We have been given an expression $15x^{\frac{1}{3}}y^{\frac{1}{5}$. We are asked to express our given expression using a radical.

Using fractional exponent rule $a^{\frac{m}{n}}=\sqrt[n]{a^m}$, we can write terms of our given expression as:

$15\cdot\sqrt[3]{x^1}\cdot \sqrt[5]{y^1}$

$15\cdot\sqrt[3]{x}\cdot \sqrt[5]{y}$

Therefore, our required expression would be $15\cdot\sqrt[3]{x}\cdot \sqrt[5]{y}$.