What is \sqrt[3]{\sqrt[4]{9m^3n^7}} ?

The solution to \sqrt[3]{\sqrt[4]{9m^3n^7}} is \sqrt[6]{3}\sqrt[12]{m^3n^7}

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simplify \sqrt[3]{\sqrt[4]{9m^3n^7}}

simplify

Solution steps

Apply radical rule:

= ((9 m^{3} n^{7})^{\frac{1}{4}})^{\frac{1}{3}}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

= (9 m^{3} n^{7})^{\frac{1}{4} \cdot \frac{1}{3}}

\frac{1}{4} \cdot \frac{1}{3} = \frac{1}{12}

= (9 m^{3} n^{7})^{\frac{1}{12}}

Apply radical rule:

assuming

a \geq 0, b \geq 0

\frac{( - 35 ) ^{7}}{5 ^{7}}

(2 x^{7}) (5 x^{2})

(32) 2

e^{- \frac{15}{10}}

x (e^{- x})

What is \sqrt[3]{\sqrt[4]{9m^3n^7}} ?
The solution to \sqrt[3]{\sqrt[4]{9m^3n^7}} is \sqrt[6]{3}\sqrt[12]{m^3n^7}