Question

1. which of the following is equivalent to (sqrt4{x^{5}})? a) (x) b) (x^{5}-x^{4}) c) (x^{\frac{5}{4}}) d) (x^{\frac{4}{5}})

Explanation:

Step1: Recall the radical to exponent rule

The rule for converting a radical to an exponent is \(\sqrt[n]{a^m}=a^{\frac{m}{n}}\). Here, we have \(\sqrt[4]{x^5}\), so \(n = 4\) and \(m = 5\).

Step2: Apply the rule

Using the rule \(\sqrt[n]{a^m}=a^{\frac{m}{n}}\), substitute \(n = 4\) and \(m = 5\) into the formula. So \(\sqrt[4]{x^5}=x^{\frac{5}{4}}\).

Answer:

C) \(x^{\frac{5}{4}}\)