The expression with a rational exponent of the seventh root of x to the third power is x to the three sevenths power ⇒ answer A
Step-by-step explanation:
Let us explain how to change the radical expression as an expression
with a rational exponent
1. Find the number of the root and make it the denominator of the
fraction exponent
2. Find the power of the term under the radical and make it the
numerator of the fraction exponent
Examples:
[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 power
The expression with a rational exponent of the seventh root of x to the third power is x to the three sevenths power
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You can learn more about radical equation is brainly.com/question/7153188
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Answer:
yes, x to the 3/7th power is correct
Step-by-step explanation:
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