What is \sqrt[22]{7^{7^7+17}} ?

The solution to \sqrt[22]{7^{7^7+17}} is 7^{37434}*7^{6/11}

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simplify \sqrt[22]{7^{7^7+17}}

simplify

7^{37434} \cdot 7^{\frac{6}{11}}

Solution steps

Apply radical rule:

= (7^{7^{7} + 17})^{\frac{1}{22}}

Apply exponent rule:

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

= 7^{(7^{7} + 17) \frac{1}{22}}

(7^{7} + 17) \frac{1}{22} = \frac{411780}{11}

= 7^{\frac{411780}{11}}

7^{\frac{411780}{11}} = 7^{37434 + \frac{6}{11}}

= 7^{37434 + \frac{6}{11}}

Apply exponent rule:

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

= 7^{37434} \cdot 7^{\frac{6}{11}}

1.9 \cdot 1 0^{- 7}

3^{3 x - 1 = 3^{x + 4}}

1.33 \cdot 1 0^{- 8}

e^{- 2 x} x^{6}

What is \sqrt[22]{7^{7^7+17}} ?
The solution to \sqrt[22]{7^{7^7+17}} is 7^{37434}*7^{6/11}