Question

simplify.
\\(\left(w^{3}\
ight)^{\frac{6}{7}}\\)
write your answer without parentheses.
assume that the variable represents a positive real number.

Explanation:

Step1: Apply the power - of - a - power rule

The power - of - a - power rule states that \((a^{m})^{n}=a^{m\times n}\). In the expression \((w^{3})^{\frac{6}{7}}\), we have \(a = w\), \(m = 3\), and \(n=\frac{6}{7}\). So we multiply the exponents: \(3\times\frac{6}{7}\).

Step2: Calculate the product of the exponents

\(3\times\frac{6}{7}=\frac{3\times6}{7}=\frac{18}{7}\). So \((w^{3})^{\frac{6}{7}}=w^{\frac{18}{7}}\)

Answer:

\(w^{\frac{18}{7}}\)