Question

what is \\(\sqrt4{7^3}\\) in exponential form?
\\(7^{\frac{3}{4}}\\)
\\(7^{\frac{4}{3}}\\)
\\(7^{-\frac{4}{3}}\\)

what is \\(6^{\frac{2}{3}}\\) in radical form?
\\(\sqrt3{6^2}\\)
\\(\sqrt2{6^3}\\)
\\(\sqrt3{6 \cdot 3}\\)

Explanation:

Convert radical to exponential form

Using the Radical to Exponential Form and Rational Exponents knowledge points

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

$$ \sqrt[4]{7^3} = 7^{\frac{3}{4}} $$

Convert exponential to radical form

Using the Rational Exponents and Radical to Exponential Form knowledge points

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

$$ 6^{\frac{2}{3}} = \sqrt[3]{6^2} $$

Answer:

Question 1

• (A) \(7^{\frac{3}{4}}\) (Correct answer)
• (B) \(7^{\frac{4}{3}}\)
• (C) \(7^{-\frac{4}{3}}\)

Question 2

• (A) \(\sqrt[3]{6^2}\) (Correct answer)
• (B) \(\sqrt[2]{6^3}\)
• (C) \(\sqrt[3]{6 \cdot 3}\)