Question

write \\((\sqrt4{81})^5\\) in exponential form.
\\(81^{\frac{5}{4}}\\)
\\(81^{\frac{4}{5}}\\)
\\(81^9\\)

simplify: \\(81^{\frac{5}{4}}\\)
3
243
6,561
59,049

write \\(\sqrt4{81^5}\\) in exponential form.
\\(81^9\\)
\\(81^{\frac{5}{4}}\\)
\\(81^{\frac{4}{5}}\\)

Explanation:

Convert first radical expression

Using the Radical to Exponential Form knowledge point

$$ (\sqrt[4]{81})^5 = (81^{1/4})^5 = 81^{5/4} $$

Simplify the exponential expression

Using the Rational Exponents and Algebraic Simplification knowledge points

$$ 81^{5/4} = (\sqrt[4]{81})^5 = 3^5 = 243 $$

Convert second radical expression

Using the Radical to Exponential Form knowledge point

$$ \sqrt[4]{81^5} = (81^5)^{1/4} = 81^{5/4} $$

Answer:

Question 1

• (A) \(81^{\frac{5}{4}}\) (Correct answer)
• (B) \(81^{\frac{4}{5}}\)
• (C) \(81^9\)

Question 2

• (A) 3
• (B) 243 (Correct answer)
• (C) 6,561
• (D) 59,049

Question 3

• (A) \(81^9\)
• (B) \(81^{\frac{5}{4}}\) (Correct answer)
• (C) \(81^{\frac{4}{5}}\)