Question

which expressions are equivalent to \frac{10}{10^{\frac{3}{4}}}?

10^{\frac{4}{3}}
10^{\frac{1}{4}}
\sqrt3{10^4}
\sqrt4{10}

Explanation:

Simplify the given expression

Using the Exponent Rules knowledge point

$$ \frac{10}{10^{\frac{3}{4}}} = \frac{10^1}{10^{\frac{3}{4}}} = 10^{1 - \frac{3}{4}} = 10^{\frac{1}{4}} $$

Evaluate the first option

Using the Exponent Rules knowledge point

$$ 10^{\frac{4}{3}} eq 10^{\frac{1}{4}} $$

Evaluate the second option

Using the Exponent Rules knowledge point

$$ 10^{-\frac{1}{4}} = \frac{1}{10^{\frac{1}{4}}} eq 10^{\frac{1}{4}} $$

Evaluate the third option

Using the Radical to Exponential Form knowledge point

$$ \sqrt[3]{10^4} = 10^{\frac{4}{3}} eq 10^{\frac{1}{4}} $$

Evaluate the fourth option

Using the Radical to Exponential Form knowledge point

$$ \sqrt[4]{10} = 10^{\frac{1}{4}} $$

Answer:

• (A) \(10^{\frac{4}{3}}\)
• (B) \(10^{-\frac{1}{4}}\)
• (C) \(\sqrt[3]{10^4}\)
• (D) \(\sqrt[4]{10}\) (Correct answer)