Question

question 4 (1 point) (03.01 lc) rewrite the expression with a rational exponent as a radical expression. 1 4 2 5 4 a. 4√4 b. 4√5 c. 4√2 d. 4√10

Explanation:

Step1: Recall radical - exponent rule

The rule for converting a rational exponent to a radical is \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\), where \(a\) is the base, \(m\) is the numerator of the exponent and \(n\) is the denominator of the exponent.
For the expression \(10^{\frac{1}{4}}\), here \(a = 10\), \(m = 1\) and \(n=4\).

Step2: Write as radical

According to the rule \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\), when \(a = 10\), \(m = 1\) and \(n = 4\), we have \(10^{\frac{1}{4}}=\sqrt[4]{10}\).

Answer:

\(\sqrt[4]{10}\)