2 Answers

Arno Fiva · Answer 1 · 2020-07-20T04:11:30+0000

Hello!

The answer is:

c.
$15\sqrt[15]{x^(5)y^(3)}$

To express the expression using a radical we must remember that:

Transforming radical to exponential form:

$\sqrt[n]{x}=x^{(1)/(n)}\\√(x)=x^{(1)/(2) }$

So, the given expression is:

$15x^{(1)/(3)}y^{(1)/(5)}$

Its radical form will be:

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

Then, the expression could be also equivalent to:

$15\sqrt[3]{x}\sqrt[5]{y}=15\sqrt[15]{x^(5)}\sqrt[15]{y^(3)}\\\\15\sqrt[15]{x^(5)}\sqrt[15]{y^(3)}=15\sqrt[15]{x^(5)y^(3)}$

Have a nice day!

Mel Green · Answer 2 · 2020-07-25T15:35:59+0000

Answer: option c

Explanation:

By definition, if you have:

$\sqrt[n]{x}$

you can rewrite it has following:

$x^{(1)/(n)}$

Therefore, keeping the above on mind, you can rewrite the expression given in the problem, as you can see below:

$15x^{(1)/(3)}y^{(1)/(5)}=(15\sqrt[3]{x})(\sqrt[5]{y})$

Both terms are multiples of 15, then take the 15th root of both and multiply the exponents by 15. Therefore you obtain:

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