Question

what is \\(\sqrt8{6}\\) in exponential form?
\\(6^8\\)
\\(6^{\frac{1}{8}}\\)
\\(8^{\frac{1}{6}}\\)

what is \\(15^{\frac{1}{3}}\\) in radical form?
\\(15\sqrt{3}\\)
\\(\sqrt\frac{1}{3}{15}\\)
\\(\sqrt3{15}\\)

Explanation:

Convert radical to exponential form

Using the Radical to Exponential Form knowledge point

$$ \sqrt[n]{a} = a^{\frac{1}{n}} $$

$$ \sqrt[8]{6} = 6^{\frac{1}{8}} $$

Convert exponential to radical form

Using the Rational Exponents knowledge point

$$ a^{\frac{1}{n}} = \sqrt[n]{a} $$

$$ 15^{\frac{1}{3}} = \sqrt[3]{15} $$

Answer:

Question 1

• (A) \(6^8\)
• (B) \(6^{\frac{1}{8}}\) (Correct answer)
• (C) \(8^{\frac{1}{6}}\)

Question 2

• (A) \(15\sqrt{3}\)
• (B) \(\frac{1}{\sqrt[3]{15}}\)
• (C) \(\sqrt[3]{15}\) (Correct answer)