What is \sqrt[22]{7^{7^7}} ?

The solution to \sqrt[22]{7^{7^7}} is 7^{37433}*7^{17/22}

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simplify \sqrt[22]{7^{7^7}}

simplify

7^{37433} \cdot 7^{\frac{17}{22}}

Solution steps

Apply radical rule:

= (7^{7^{7}})^{\frac{1}{22}}

Apply exponent rule:

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

= 7^{7^{7} \cdot \frac{1}{22}}

7^{7} \cdot \frac{1}{22} = \frac{823543}{22}

= 7^{\frac{823543}{22}}

7^{\frac{823543}{22}} = 7^{37433 + \frac{17}{22}}

= 7^{37433 + \frac{17}{22}}

Apply exponent rule:

x^{a + b} = x^{a} x^{b}

= 7^{37433} \cdot 7^{\frac{17}{22}}

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What is \sqrt[22]{7^{7^7}} ?
The solution to \sqrt[22]{7^{7^7}} is 7^{37433}*7^{17/22}