Certainly! Let's rewrite the given expression [tex]\( 7x^{\frac{2}{3}} \)[/tex] as a radical expression step-by-step.
### Understanding Rational Exponents
Rational exponents can be interpreted using radicals. The general rule is:
[tex]\[ a^{\frac{m}{n}} = \sqrt[n]{a^m} \][/tex]
### Given Expression
We are given the expression [tex]\( 7x^{\frac{2}{3}} \)[/tex].
### Applying the Rule
- [tex]\( x^{\frac{2}{3}} \)[/tex] can be rewritten using the rule above:
[tex]\[ x^{\frac{2}{3}} = \sqrt[3]{x^2} \][/tex]
### Incorporating the Coefficient
- The given expression has an additional coefficient of 7:
[tex]\[ 7x^{\frac{2}{3}} = 7 \cdot x^{\frac{2}{3}} \][/tex]
[tex]\[ 7x^{\frac{2}{3}} = 7 \cdot \sqrt[3]{x^2} \][/tex]
### Final Radical Expression
The expression [tex]\( 7x^{\frac{2}{3}} \)[/tex] is correctly rewritten as:
[tex]\[ 7 \sqrt[3]{x^2} \][/tex]
### Conclusion
So, the correct radical expression corresponding to [tex]\( 7x^{\frac{2}{3}} \)[/tex] is:
[tex]\[ 7 \sqrt[3]{x^2} \][/tex]
