Question

Rewrite the expression with rational exponents as a radical expression by extending the properties of i tiger exponents

Answer 1

Answer:

$\sqrt[6]{y}$

Step-by-step explanation:

The expression is

$\frac{y^{\frac{1}{3} } }{y^{\frac{1}{6}}}$

Applying rule of exponents, $\frac{x^{m}}{x^{n}}=x^{m-n}$

$\frac{y^{\frac{1}{3} } }{y^{\frac{1}{6}}}=y^{\frac{1}{3}-\frac{1}{6}}=y^{\frac{2-1}{6}}=y^{\frac{1}{6}}$

Now,we know that, $x^{\frac{1}{n}}=\sqrt[n]{x}$

∴ $y^{\frac{1}{6}}=\sqrt[6]{y}$

So, the last option is correct.