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Write the expression in radical form. Assume that the variable represents a positive real number.

[tex]\[ 2 c^{8/9} \][/tex]

[tex]\[ 2 c^{8/9} = \sqrt[9]{c^8} \][/tex]

(Do not simplify.)


Sagot :

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]