Question

simplify. assume all variables are positive.
\\(\frac{b^{\frac{1}{7}}}{b^{\frac{11}{7}}}\\)
write your answer in the form a or \\(\frac{a}{b}\\), where a and b are constants or variable expressions that have no variables in common. all exponents in your answer should be positive.

Explanation:

Step1: Use exponent - division rule

When dividing two powers with the same base \(a^m\div a^n=a^{m - n}\), here \(a = b\), \(m=\frac{1}{7}\), and \(n=\frac{11}{7}\). So \(\frac{b^{\frac{1}{7}}}{b^{\frac{11}{7}}}=b^{\frac{1}{7}-\frac{11}{7}}\).

Step2: Calculate the exponent

\(\frac{1}{7}-\frac{11}{7}=\frac{1 - 11}{7}=\frac{- 10}{7}\). Since we need positive exponents, \(b^{-\frac{10}{7}}=\frac{1}{b^{\frac{10}{7}}}\).

Answer:

\(\frac{1}{b^{\frac{10}{7}}}\)