To express the given expression [tex]\(2c^{\frac{8}{9}}\)[/tex] in radical form, here's a step-by-step explanation:
1. Identify the exponent:
The exponent in the given expression [tex]\(2c^{\frac{8}{9}}\)[/tex] is [tex]\(\frac{8}{9}\)[/tex].
2. Rewrite the exponent:
Recall that [tex]\(c^{\frac{m}{n}} = \sqrt[n]{c^m}\)[/tex]. Here, [tex]\(\frac{m}{n} = \frac{8}{9}\)[/tex], so [tex]\(m=8\)[/tex] and [tex]\(n=9\)[/tex].
3. Express the exponent in radical form:
Using the relationship above, [tex]\(c^{\frac{8}{9}}\)[/tex] can be rewritten as [tex]\(\sqrt[9]{c^8}\)[/tex].
4. Recombine with the constant factor:
The given expression [tex]\(2c^{\frac{8}{9}}\)[/tex] becomes:
[tex]\[
2 \sqrt[9]{c^8}
\][/tex]
Thus, the expression [tex]\(2c^{\frac{8}{9}}\)[/tex] written in radical form is [tex]\(2 \sqrt[9]{c^8}\)[/tex].
So, we have:
[tex]\[
2c^{8/9} = 2 \sqrt[9]{c^8}
\][/tex]
