To write the expression [tex]\( c^{\frac{6}{5}} \)[/tex] as a radical expression, we can use the properties of rational exponents. Here's a detailed step-by-step solution:
1. Understanding Rational Exponents:
- A rational exponent of [tex]\( \frac{a}{b} \)[/tex] can be interpreted as the b-th root of the base raised to the power a. In general terms, [tex]\( x^{\frac{a}{b}} \)[/tex] is equivalent to [tex]\( \sqrt[b]{x^a} \)[/tex].
2. Apply the Property:
- In our case, the base is [tex]\( c \)[/tex], the numerator [tex]\( a \)[/tex] of the exponent is 6, and the denominator [tex]\( b \)[/tex] is 5. So, we start by recognizing the pattern [tex]\( c^{\frac{a}{b}} = \sqrt[b]{c^a} \)[/tex].
3. Rewrite the Exponent:
- Substitute [tex]\( a \)[/tex] with 6 and [tex]\( b \)[/tex] with 5 into the pattern: [tex]\( c^{\frac{6}{5}} = \sqrt[5]{c^6} \)[/tex].
4. Conclusion:
- Therefore, the expression [tex]\( c^{\frac{6}{5}} \)[/tex] when written as a radical expression becomes [tex]\( \sqrt[5]{c^6} \)[/tex].
Hence, the radical expression for [tex]\( c^{\frac{6}{5}} \)[/tex] is:
[tex]$
\boxed{\sqrt[5]{c^6}}
$[/tex]
