Question

simplify
plz give answer

Answer 1

$\mathfrak{Question:}$

$\large\tt{\sqrt[5]{x^4\sqrt[4]{x^3\sqrt[3]{x^2\sqrt{x}}}}.}$

$\mathfrak{Answer:}$

$\bold{=x^{\frac{119}{120}}.}$

$\mathfrak{Step-by-Step\:Explanation:}$

$\large\tt{=\sqrt[5]{x^4\sqrt[4]{x^3\sqrt[3]{x^2\sqrt{x}}}}}\\\\\\\large\tt{=\sqrt[5]{x^4\sqrt[4]{x^3\sqrt[3]{x^2\times x^{\frac{1}{2}}}}}}\\\\\\\large\tt{=\sqrt[5]{x^4\sqrt[4]{x^3\sqrt[3]{ x^{2+\frac{1}{2}}}}}}\\\\\\\large\tt{=\sqrt[5]{x^4\sqrt[4]{x^3\sqrt[3]{ x^{\frac{5}{2}}}}}}\\\\\\\large\tt{=\sqrt[5]{x^4\sqrt[4]{x^3\times{x^{\frac{5}{2\times3}}}}}}\\\\\\\large\tt{=\sqrt[5]{x^4\sqrt[4]{x^3\times{x^{\frac{5}{6}}}}}}\\\\\\\large\tt{=\sqrt[5]{x^4\sqrt[4]{{x^{3+\frac{5}{6}}}}}}$

$\large\tt{=\sqrt[5]{x^4\sqrt[4]{{x^{\frac{23}{6}}}}}}\\\\\\\large\tt{=\sqrt[5]{x^4\times{{x^{\frac{23}{6\times 4}}}}}}\\\\\\\large\tt{=\sqrt[5]{{{x^{4+\frac{23}{24}}}}}}\\\\\\\large\tt{=\sqrt[5]{{{x^{\frac{119}{24}}}}}}\\\\\\\large\tt{={{{x^{\frac{119}{24\times 5}}}}}}\\\\\\\tt{=x^{\frac{119}{120}}}.$

$\boxed{\boxed{\bold{\large\tt{\sqrt[5]{x^4\sqrt[4]{x^3\sqrt[3]{x^2\sqrt{x}}}}=x^{\frac{119}{120}}}.}}}$

Answer 2

Solution :

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

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

$= > \sqrt[5]{x^{4} \sqrt[4]{x ^{3} \times \: x \frac{5}{6} } } = \sqrt[5]{x^{4} \sqrt[4]{x \frac{23}{6} } }$

$= > \sqrt[5]{x^{4} \times x \frac{23}{6 \times 4} } = \sqrt[5]{x^{4} + \frac{23}{24} }$

$= > \sqrt[5]{x \frac{119}{24} } = x \frac{119}{24 \times 5}$

$= > x \frac{119}{120}$

Hence ,

$= > \sqrt[5]{x^{4} \sqrt[4]{x^{3} \sqrt[3]{x^{2} \sqrt{x } } } } = x \frac{119}{120}$