Question

lesson 11.2 checkpoint
once you have completed the above by c
below.
complete the lesson reflection above by c
simplify each expression. assume all variables a

1. $\frac{x^{\frac{1}{3}}cdot x^{\frac{1}{5}}}{x^{\frac{1}{6}}}$

Explanation:

Step1: Use exponent - product rule

When multiplying powers with the same base \(a^m\cdot a^n=a^{m + n}\), so \(x^{\frac{1}{3}}\cdot x^{\frac{5}{6}}=x^{\frac{1}{3}+\frac{5}{6}}\).
\[x^{\frac{1}{3}+\frac{5}{6}}=x^{\frac{2 + 5}{6}}=x^{\frac{7}{6}}\]

Step2: Use exponent - quotient rule

When dividing powers with the same base \(\frac{a^m}{a^n}=a^{m - n}\), so \(\frac{x^{\frac{7}{6}}}{x^{\frac{1}{6}}}=x^{\frac{7}{6}-\frac{1}{6}}\).
\[x^{\frac{7}{6}-\frac{1}{6}}=x^{\frac{7 - 1}{6}}=x\]

Answer:

\(x\)