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{y^{\frac{b}{2}}}{y^{\frac{3}{2}}}=\\)

Explanation:

Step1: Apply exponent - division rule

When dividing two exponential expressions with the same base \(a^m\div a^n=a^{m - n}\), here \(a = y\), \(m=\frac{b}{2}\), and \(n=\frac{3}{2}\). So \(\frac{y^{\frac{b}{2}}}{y^{\frac{3}{2}}}=y^{\frac{b}{2}-\frac{3}{2}}\).

Step2: Simplify the exponent

\(\frac{b}{2}-\frac{3}{2}=\frac{b - 3}{2}\), so \(y^{\frac{b}{2}-\frac{3}{2}}=y^{\frac{b - 3}{2}}\).

Answer:

\(y^{\frac{b - 3}{2}}\)