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

The solution to \sqrt[22]{7^{7^7+22}} is 7^{37434}*7^{17/22}

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

simplify

7^{37434} \cdot 7^{\frac{17}{22}}

Solution steps

Apply radical rule:

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

Apply exponent rule:

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

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

(7^{7} + 22) \frac{1}{22} = \frac{823565}{22}

= 7^{\frac{823565}{22}}

7^{\frac{823565}{22}} = 7^{37434 + \frac{17}{22}}

= 7^{37434 + \frac{17}{22}}

Apply exponent rule:

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

= 7^{37434} \cdot 7^{\frac{17}{22}}

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What is \sqrt[22]{7^{7^7+22}} ?
The solution to \sqrt[22]{7^{7^7+22}} is 7^{37434}*7^{17/22}