Question

8.3 simplify rational exponents (homework)
score: 15.05/25 answered: 16/25
question 17
simplify by writing as a single exponential expression. assume all variables are positive.
\\(\frac{b^{\frac{3}{5}}}{b^{\frac{4}{5}}}=\\)
question help: video written example

Explanation:

Step1: Use exponent - division rule

When dividing two exponential expressions with the same base \(a^m\div a^n=a^{m - n}\), here \(a = b\), \(m=\frac{3}{5}\), and \(n=\frac{4}{5}\). So \(\frac{b^{\frac{3}{5}}}{b^{\frac{4}{5}}}=b^{\frac{3}{5}-\frac{4}{5}}\).

Step2: Calculate the exponent

\(\frac{3}{5}-\frac{4}{5}=\frac{3 - 4}{5}=-\frac{1}{5}\). So \(b^{\frac{3}{5}-\frac{4}{5}}=b^{-\frac{1}{5}}\).

Step3: Rewrite negative - exponent

Using the rule \(a^{-n}=\frac{1}{a^{n}}\), we can rewrite \(b^{-\frac{1}{5}}\) as \(\frac{1}{b^{\frac{1}{5}}}\).

Answer:

\(b^{-\frac{1}{5}}\) or \(\frac{1}{b^{\frac{1}{5}}}\)