Question

simplify 10^(1/ 3)n × 15^(1/ 2)n × 6^(1/6)n ÷ 45^(1/3)n

Answer 1

Solution

$\dfrac{10^{\frac{1}{3}n}\cdot15^{\frac{1}{2}n}\cdot6^{\frac{1}{6}n}}{45^{\frac{1}{3}n}} = \left(\dfrac{2^\frac{1}{3}5^\frac{1}{3}\cdot3^\frac{1}{2}5^\frac{1}{2}\cdot2^\frac{1}{6}3^\frac{1}{6}}{3^\frac{2}{3}5^\frac{1}{3}}\right)^n =$

$=\left(2^{\left(\frac{1}{3}+\frac{1}{6}\right)}\cdot3^{\left(\frac{1}{2}+\frac{1}{6}-\frac{2}{3}\right)}\cdot5^{\left(\frac{1}{3}+\frac{1}{2}-\frac{1}{3}\right)}\right)^n = \left(2^{\frac{1}{2}}\cdot3^0\cdot5^{\frac{1}{2}} \right)^n = \left(\sqrt{10}\right)^n$

Answer

10^(1/2)n