Question

please help :( I know that lt="2^\frac{6}{5}" align="absmiddle" class="latex-formula"> is the same as $2\sqrt[5]{2}$ but I don't understand how to get $2\sqrt[5]{2}$ from $2^\frac{6}{5}$

Answer 1

Answer:

$\displaystyle 2^{\frac{6}{5}}=2\sqrt[5]{2}$

Step-by-step explanation:

Fractional Exponents

An expression like

$\displaystyle a^{\frac{n}{m}}$

can be expressed as a radical of the form:

$\sqrt[m]{a^n}$

We have the expression:

$\displaystyle 2^{\frac{6}{5}}$

Its equivalent radical form is:

$\displaystyle 2^{\frac{6}{5}}=\sqrt[5]{2^6}$

Since the exponent is greater than the index of the radical, we can take 2 out of it by following the procedure:

$\sqrt[5]{2^6}=\sqrt[5]{2^5\cdot 2}$

Taking out $2^5$ from the radical:

$\sqrt[5]{2^6}=2\sqrt[5]{2}$

Thus:

$\displaystyle 2^{\frac{6}{5}}=2\sqrt[5]{2}$