Answer :
To convert [tex]\(6^{\frac{2}{3}}\)[/tex] into radical form, let's follow these steps:
1. Exponent Representation: We start with the expression [tex]\(6^{\frac{2}{3}}\)[/tex].
2. Fractional Exponent: The exponent [tex]\(\frac{2}{3}\)[/tex] indicates that we're dealing with both a root and a power. Specifically:
- The denominator (3) represents the root.
- The numerator (2) represents the power.
3. Radical Form Transformation:
- First, we rewrite [tex]\(6^{\frac{2}{3}}\)[/tex] to emphasize the root and power: [tex]\((6^2)^{\frac{1}{3}}\)[/tex].
- This is equivalent to the cube root of [tex]\(6^2\)[/tex], which can be written as [tex]\(\sqrt[3]{6^2}\)[/tex].
4. Simplified Radical Form: We conclude that [tex]\(6^{\frac{2}{3}}\)[/tex] is [tex]\(\sqrt[3]{6^2}\)[/tex] in radical form.
Therefore, the correct answer is [tex]\(\sqrt[3]{6^2}\)[/tex].
1. Exponent Representation: We start with the expression [tex]\(6^{\frac{2}{3}}\)[/tex].
2. Fractional Exponent: The exponent [tex]\(\frac{2}{3}\)[/tex] indicates that we're dealing with both a root and a power. Specifically:
- The denominator (3) represents the root.
- The numerator (2) represents the power.
3. Radical Form Transformation:
- First, we rewrite [tex]\(6^{\frac{2}{3}}\)[/tex] to emphasize the root and power: [tex]\((6^2)^{\frac{1}{3}}\)[/tex].
- This is equivalent to the cube root of [tex]\(6^2\)[/tex], which can be written as [tex]\(\sqrt[3]{6^2}\)[/tex].
4. Simplified Radical Form: We conclude that [tex]\(6^{\frac{2}{3}}\)[/tex] is [tex]\(\sqrt[3]{6^2}\)[/tex] in radical form.
Therefore, the correct answer is [tex]\(\sqrt[3]{6^2}\)[/tex].
