Question

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

Explanation:

Step1: Recall radical to exponential rule

The \(n\)-th root of a number \(a\) is \(a^{\frac{1}{n}}\), and \(\frac{1}{\sqrt[n]{a^m}}=a^{-\frac{m}{n}}\).
For \(\sqrt[7]{x^{15}}\), using the rule \(\sqrt[n]{a^m}=a^{\frac{m}{n}}\), we have \(\sqrt[7]{x^{15}} = x^{\frac{15}{7}}\). Then \(\frac{1}{\sqrt[7]{x^{15}}}=x^{-\frac{15}{7}}\).

Step2: Multiply by the constant

The original expression is \(\frac{8}{\sqrt[7]{x^{15}}}\), so multiplying 8 with \(x^{-\frac{15}{7}}\) gives \(8x^{-\frac{15}{7}}\).

Answer:

B. \(8x^{-\frac{15}{7}}\)