Question

Simply $\frac{\sqrt[3]{162x^{2} } }{\sqrt[3]{2x} }$

Answer 1

Answer:

$\large\boxed{\sf{3 \sqrt[3]{3x} }}$

Step-by-step explanation:

$\dfrac{\sqrt[3]{162x^{2} } }{\sqrt[3]{2x} } \\ \\ = \sqrt[3]{ \dfrac{162 {x}^{ \cancel{2}} }{2 \cancel{x}} } \\ \\ = \sqrt[3]{ \frac{162x}{2} } \\ \\ = \sqrt[3]{81x} \\ \\ = \sqrt[3]{81} \times \sqrt[3]{x} \\ \\ = \sqrt[3]{ {3}^{4} } \times \sqrt[3]{x } \\ \\ = { ({3}^{4} )}^{ \frac{1}{3} } \times {x}^{ \frac{1}{3} } \\ \\ = {(3)}^{ \frac{4}{3} } {(x)}^{ \frac{1}{3} } \\ \\ = {(3)}^{(1 + \frac{1}{3}) } \times {(x)}^{ \frac{1}{3} } \\ \\ = {3}^{1} \times {3}^{ \frac{1}{3} } \times {x}^{ \frac{1}{3} } \\ \\ = 3 \times {(3x)}^{ \frac{1}{3} } \\ \\ = 3 \sqrt[3]{3x}$

Concept Map :-

• $\sqrt[n]{x} = {x}^{ \frac{1}{n} }$

• $\sqrt{xy} = \sqrt{x} \times \sqrt{y}$

• ${x}^{(m + n)} = {x}^{m} \times {x}^{n}$

• ${(xy)}^{m} = {x}^{m} \times {y}^{m}$