Question

Simplify
$\sqrt[5]{ {x}^{4} \sqrt[4]{ {x^{3} \sqrt[3]{x ^{2} \sqrt{x} } }} }}$

Answer 1

$\sf{Simplify\: :\: \: \sqrt[5]{ {x}^{4} \sqrt[4]{ {x^{3} \sqrt[3]{x ^{2} \sqrt{x} } }} }}$

$\sf{Answer=\gray{x ^ { \frac{119}{120} }} }$

Step by step explanation

$\sf\Longrightarrow\sqrt[5]{ {x}^{4} \sqrt[4]{ {x^{3} \sqrt[3]{x ^{2} \sqrt{x} } }} }$

$\sf\Longrightarrow\sqrt[5]{ {x}^{4} \sqrt[4]{ {x^{3} \sqrt[3]{x ^{2} \times {x}^{ \frac{1}{2} } } }} }$

$\sf\Longrightarrow\sqrt[5]{ {x}^{4} \sqrt[4]{ {x^{3} \sqrt[3]{x ^{ \frac{5}{2} } } }} }$

$\sf\Longrightarrow\sqrt[5]{ {x}^{4} \sqrt[4]{ {x^{3} \sqrt{x ^{ \frac{5}{2 \times 3} } } }} }$

$\sf\Longrightarrow\sqrt[5]{ {x}^{4} \: \sqrt[4]{ {x^{3} \times {x ^{ \frac{5}{6} } } }} }$

$\sf\Longrightarrow\sqrt[5]{ {x}^{4} \: \sqrt[4]{ {x ^ { \frac{23}{6}} } } }$

$\sf\Longrightarrow\sqrt[5]{ {x}^{4} \: \times { {x ^ { \frac{23}{6 \times 4}} } } }$

$\sf\Longrightarrow\sqrt[5]{ {x}^{4} \: \times { {x ^ { \frac{23}{24}} } } }$

$\sf\Longrightarrow\sqrt[5]{ { {x ^ { \frac{119}{24} }} } }$

$\sf\Longrightarrow\sqrt{ { {x ^ { \frac{119}{24 \times 5} }} } }$

$\sf\Longrightarrow{x ^ { \dfrac{119}{120} }}$

Answer 2

Step-by-step explanation:

$\sf{Simplify\: :\: \: \sqrt[5]{ {x}^{4} \sqrt[4]{ {x^{3} \sqrt[3]{x ^{2} \sqrt{x} } }} }}Simplify:5x44x33x2x \\ </p><p></p><p>\sf{Answer=\gray{x ^ { \frac{119}{120} }} }Answer=x120119 \\ </p><p></p><p>Step by step explanation \\ </p><p></p><p>\sf\Longrightarrow\sqrt[5]{ {x}^{4} \sqrt[4]{ {x^{3} \sqrt[3]{x ^{2} \sqrt{x} } }} }⟹5x44x33x2x \\ </p><p></p><p>\sf\Longrightarrow\sqrt[5]{ {x}^{4} \sqrt[4]{ {x^{3} \sqrt[3]{x ^{2} \times {x}^{ \frac{1}{2} } } }} }⟹5x44x33x2×x21 \\ </p><p></p><p>\sf\Longrightarrow\sqrt[5]{ {x}^{4} \sqrt[4]{ {x^{3} \sqrt[3]{x ^{ \frac{5}{2} } } }} }⟹5x44x33x25 \\ </p><p></p><p>\sf\Longrightarrow\sqrt[5]{ {x}^{4} \sqrt[4]{ {x^{3} \sqrt{x ^{ \frac{5}{2 \times 3} } } }} }⟹5x44x3x2×35 \\ </p><p></p><p>\sf\Longrightarrow\sqrt[5]{ {x}^{4} \: \sqrt[4]{ {x^{3} \times {x ^{ \frac{5}{6} } } }} }⟹5x44x3×x65 \\ </p><p></p><p>\sf\Longrightarrow\sqrt[5]{ {x}^{4} \: \sqrt[4]{ {x ^ { \frac{23}{6}} } } }⟹5x44x623 \\ </p><p></p><p>\sf\Longrightarrow\sqrt[5]{ {x}^{4} \: \times { {x ^ { \frac{23}{6 \times 4}} } } }⟹5x4×x6×423 \\ </p><p></p><p>\sf\Longrightarrow\sqrt[5]{ {x}^{4} \: \times { {x ^ { \frac{23}{24}} } } }⟹5x4×x2423 \\ </p><p></p><p>\sf\Longrightarrow\sqrt[5]{ { {x ^ { \frac{119}{24} }} } }⟹5x24119 \\ </p><p></p><p>\sf\Longrightarrow\sqrt{ { {x ^ { \frac{119}{24 \times 5} }} } }⟹x24×5119 \\ </p><p></p><p>\sf\Longrightarrow{x ^ { \dfrac{119}{120} }}⟹x120119</p><p></p><p>$