7..........................

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carlosego carlosego · Answer 1 · 2019-03-29T17:59:47+01:00

Answer: option c

Step-by-step explanation:

By definition, if you have:

[tex]\sqrt[n]{x}[/tex]

you can rewrite it has following:

[tex]x^{\frac{1}{n}}[/tex]

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

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

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

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

mixter17 mixter17 · Answer 2 · 2019-03-29T18:56:42+01:00

The answer is:

c. [tex]15\sqrt[15]{x^{5}y^{3}}[/tex]

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

Transforming radical to exponential form:

[tex]\sqrt[n]{x}=x^{\frac{1}{n}}\\\sqrt{x}=x^{\frac{1}{2} }[/tex]

So, the given expression is:

[tex]15x^{\frac{1}{3}}y^{\frac{1}{5}}[/tex]

Its radical form will be:

[tex]15\sqrt[3]{x}\sqrt[5]{y}[/tex]

Then, the expression could be also equivalent to:

[tex]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}}[/tex]

Have a nice day!