To solve the expression [tex]\(\sqrt[3]{c^2}\)[/tex], we need to find the cube root of [tex]\(c^2\)[/tex].
Here's a step-by-step breakdown:
1. Understand the Expression: [tex]\(\sqrt[3]{c^2}\)[/tex] denotes the cube root of [tex]\(c^2\)[/tex]. This means we are looking for a number which, when raised to the power of three, gives [tex]\(c^2\)[/tex].
2. Rewrite in Exponential Form: The cube root of [tex]\(c^2\)[/tex] can be written in exponential form as [tex]\((c^2)^{1/3}\)[/tex]. This is because the cube root is equivalent to raising the number to the power of [tex]\(\frac{1}{3}\)[/tex].
3. Apply the Exponent Rules: According to the laws of exponents, [tex]\((a^m)^n = a^{m \cdot n}\)[/tex]. So, [tex]\((c^2)^{1/3}\)[/tex] can be simplified by multiplying the exponents:
[tex]\[
(c^2)^{1/3} = c^{2 \cdot \frac{1}{3}} = c^{\frac{2}{3}}
\][/tex]
4. Final Answer: Therefore, the expression [tex]\(\sqrt[3]{c^2}\)[/tex] simplifies to [tex]\(c^{\frac{2}{3}}\)[/tex].
So, the final solution to the expression [tex]\(\sqrt[3]{c^2}\)[/tex] is [tex]\(c^{\frac{2}{3}}\)[/tex].
