Question

8.3 simplify rational exponents (homework) score: 14.05/25 answered: 15/25 question 16 simplify by writing as a single exponential expression. assume all variables are positive. $x^{\frac{3}{2}}x^{\frac{1}{2}}=$ question help: video written example

Explanation:

Step1: Apply exponent - product rule

When multiplying two exponential expressions with the same base \(a^m\times a^n=a^{m + n}\), here \(a = x\), \(m=\frac{3}{2}\), and \(n=\frac{1}{2}\). So \(x^{\frac{3}{2}}x^{\frac{1}{2}}=x^{\frac{3}{2}+\frac{1}{2}}\).

Step2: Add the exponents

Calculate \(\frac{3}{2}+\frac{1}{2}=\frac{3 + 1}{2}=\frac{4}{2}=2\). So \(x^{\frac{3}{2}+\frac{1}{2}}=x^{2}\).

Answer:

\(x^{2}\)