Question

lesson 11.2 checkpoint
once you have completed the above problems and checked your solutions, complete the lesson checkpoint below.
complete the lesson reflection above by circling your current understanding of the learning goal.
simplify each expression. assume all variables are positive.

1. $\frac{x^{\frac{1}{3}}cdot x^{\frac{5}{6}}}{x^{\frac{1}{6}}}$
2. $5sqrt{125x^{4}y^{3}z}$
3. $sqrt3{\frac{125}{64}}$

Explanation:

Step1: Use exponent - product rule for the numerator

$x^{\frac{1}{3}}\cdot x^{\frac{5}{6}}=x^{\frac{1}{3}+\frac{5}{6}}=x^{\frac{2 + 5}{6}}=x^{\frac{7}{6}}$

Step2: Use exponent - quotient rule

$\frac{x^{\frac{7}{6}}}{x^{\frac{1}{6}}}=x^{\frac{7}{6}-\frac{1}{6}}=x^{\frac{7 - 1}{6}}=x$

Step1: Simplify the square - root of the coefficient

$\sqrt{125}=5\sqrt{5}$

Step2: Apply the square - root to variables

$\sqrt{x^{4}}=x^{2}$, $\sqrt{y^{3}}=y\sqrt{y}$

Step3: Combine the terms

$5\sqrt{125x^{4}y^{3}z}=5\times5\sqrt{5}x^{2}y\sqrt{y}\sqrt{z}=25x^{2}y\sqrt{5yz}$

Step1: Find the cube - root of the numerator and denominator

$\sqrt[3]{125}=5$, $\sqrt[3]{64}=4$

Answer:

$x$