Answer:
[tex]\displaystyle 2^{\frac{6}{5}}=2\sqrt[5]{2}[/tex]
Step-by-step explanation:
Fractional Exponents
An expression like
[tex]\displaystyle a^{\frac{n}{m}}[/tex]
can be expressed as a radical of the form:
[tex]\sqrt[m]{a^n}[/tex]
We have the expression:
[tex]\displaystyle 2^{\frac{6}{5}}[/tex]
Its equivalent radical form is:
[tex]\displaystyle 2^{\frac{6}{5}}=\sqrt[5]{2^6}[/tex]
Since the exponent is greater than the index of the radical, we can take 2 out of it by following the procedure:
[tex]\sqrt[5]{2^6}=\sqrt[5]{2^5\cdot 2}[/tex]
Taking out [tex]2^5[/tex] from the radical:
[tex]\sqrt[5]{2^6}=2\sqrt[5]{2}[/tex]
Thus:
[tex]\displaystyle 2^{\frac{6}{5}}=2\sqrt[5]{2}[/tex]
