Respuesta :

luisejr77

Answer: [tex]\sqrt[6]{2}[/tex]

Step-by-step explanation:

You know that the expression is [tex]\frac{\sqrt{2}}{\sqrt[3]{2}}[/tex]

By definition we know that:

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

You also need to remember the Quotient of powers property:

[tex]\frac{a^n}{a^m}=a^{(n-m)}[/tex]

Therefore, you can rewrite the expression:

[tex]=\frac{2^{\frac{1}{2}}}{2^{\frac{1}{3}}}[/tex]

Finally, you have to simplify the expression. Therefore, you get:

[tex]=2^{(\frac{1}{2}-\frac{1}{3})}\\=2^{\frac{1}{6}}\\=\sqrt[6]{2}[/tex]

kudzordzifrancis

ANSWER

[tex]\frac{ \sqrt{2} }{ \sqrt[3]{2} } = \sqrt[6]{2} [/tex]

EXPLANATION

We want to simplify

[tex] \frac{ \sqrt{2} }{ \sqrt[3]{2} } [/tex]

We rewrite in exponential form to get:

[tex]\frac{ \sqrt{2} }{ \sqrt[3]{2} } = \frac{ {2}^{ \frac{1}{2} } }{{2}^{ \frac{1}{3} } } [/tex]

Recall the quotient rule of exponents:

[tex] \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} [/tex]

We apply this rule to get:

[tex]\frac{ \sqrt{2} }{ \sqrt[3]{2} } = {2}^{ \frac{1}{2} - \frac{1}{3} } [/tex]

Simplify:

[tex] \frac{ \sqrt{2} }{ \sqrt[3]{2} } = {2}^{ \frac{3 - 2}{6} } [/tex]

[tex] \frac{ \sqrt{2} }{ \sqrt[3]{2} } = {2}^{ \frac{1}{6} } [/tex]

[tex] \frac{ \sqrt{2} }{ \sqrt[3]{2} } = \sqrt[6]{2} [/tex]

Otras preguntas