Rewrite the radical expression as an expression with a rational exponent. the seventh root of x to the third power Options:A: x to the three sevenths powerB: x to the seven thirds powerC: x21 D: x4

The expression with a rational exponent of the seventh root of x to the third power is x to the three sevenths power ⇒ answer AStep-by-step explanation:Let us explain how to change the radical expression as an expressionwith a rational exponent1. Find the number of the root and make it the denominator of the   fraction exponent2. Find the power of the term under the radical and make it the    numerator of the fraction exponentExamples:[tex]\sqrt{x^{n}}=x^{\frac{n}{2}}[/tex][tex]\sqrt[3]{x^{n}}=x^{\frac{n}{3}}[/tex][tex]\sqrt[5]{x^{n}}=x^{\frac{n}{5}}[/tex]So [tex]\sqrt[m]{x^{n}}=x^{\frac{n}{m}}[/tex]∵ the radical expression is the seventh root of x to the third power∵ seventh root = [tex]\sqrt[7]{}[/tex]∵ x to the third power = x³∴ seventh root of x to the third power = [tex]\sqrt[7]{x^{3}}[/tex]Let us change it to the rational exponent∵ [tex]\sqrt[m]{x^{n}}=x^{\frac{n}{m}}[/tex]∵ [tex]\sqrt[7]{x^{3}}[/tex]∴ m = 7 and n = 3∴ [tex]\sqrt[7]{x^{3}}[/tex] = [tex]x^{\frac{3}{7}}[/tex]∵ [tex]x^{\frac{3}{7}}[/tex] is x to the three sevenths power∴ [tex]\sqrt[7]{x^{3}}[/tex] is x to the three sevenths powerThe expression with a rational exponent of the seventh root of x to the third power is x to the three sevenths powerLearn more:You can learn more about radical equation is brainly.com/question/7153188#LearnwithBrainly