Question

6 write the radical expression \\( \frac{8}{\sqrt7{x^{15}}} \\) in exponential form. \\( \boldsymbol{\text{a}} \\) \\( 8x^{\frac{7}{15}} \\) \\( \boldsymbol{\text{b}} \\) \\( 8x^{-\frac{15}{7}} \\) \\( \boldsymbol{\text{c}} \\) \\( 8x^{-\frac{1}{15}} \\) \\( \boldsymbol{\text{d}} \\) \\( 8x^{\frac{15}{7}} \\)

Explanation:

Step1: Recall radical to exponential rule

The nth root of \( x^m \) is \( x^{\frac{m}{n}} \), and \( \frac{1}{\sqrt[n]{x^m}} = x^{-\frac{m}{n}} \).

Step2: Apply the rule to the denominator

For \( \sqrt[7]{x^{10}} \), it is \( x^{\frac{10}{7}} \), so \( \frac{1}{\sqrt[7]{x^{10}}} = x^{-\frac{10}{7}} \).

Step3: Multiply by the numerator

The original expression is \( \frac{8}{\sqrt[7]{x^{10}}} = 8\times x^{-\frac{10}{7}} = 8x^{-\frac{10}{7}} \).

Answer:

B. \( 8x^{-\frac{10}{7}} \)