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Popular >

simplify sqrt(7^{7^7)}

Solution

simplify

7^{7^{7}}

Solution

7^{411771} 7

Solution steps

7^{7^{7}}

Apply radical rule:

a = a^{\frac{1}{2}}

= (7^{7^{7}})^{\frac{1}{2}}

Apply exponent rule:

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

= 7^{7^{7} \cdot \frac{1}{2}}

7^{7} \cdot \frac{1}{2} = \frac{823543}{2}

= 7^{\frac{823543}{2}}

7^{\frac{823543}{2}} = 7^{411771 + \frac{1}{2}}

= 7^{411771 + \frac{1}{2}}

Apply exponent rule:

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

= 7^{411771} \cdot 7^{\frac{1}{2}}

Refine

= 7^{411771} 7

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Frequently Asked Questions (FAQ)

What is sqrt(7^{7^7)} ?
The solution to sqrt(7^{7^7)} is 7^{411771}sqrt(7)