What is sqrt(1000000000000^{1000000000^{10)}} ?

The solution to sqrt(1000000000000^{1000000000^{10)}} is 1000000000000^{(1000000000^{10})/2}

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simplify sqrt(1000000000000^{1000000000^{10)}}

simplify

100000000000 0^{100000000 0^{10}}

100000000000 0^{\frac{100000000 0 ^{10}}{2}}

Solution steps

100000000000 0^{100000000 0^{10}}

Apply radical rule:

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

= (100000000000 0^{100000000 0^{10}})^{\frac{1}{2}}

Apply exponent rule:

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

= 100000000000 0^{100000000 0^{10} \cdot \frac{1}{2}}

100000000 0^{10} \cdot \frac{1}{2} = \frac{100000000 0 ^{10}}{2}

= 100000000000 0^{\frac{100000000 0 ^{10}}{2}}

e^{\frac{1}{2} - 6 x} \cdot 6 e^{\frac{1}{2} + 6 x}

- e^{- x} \cdot 9 e^{3 x}

e^{- \frac{26}{450}}

7.5 \cdot 1 0^{- 1}

1500 \cdot e^{- 2000 \cdot (\frac{1}{513.15} - \frac{1}{289})}

What is sqrt(1000000000000^{1000000000^{10)}} ?
The solution to sqrt(1000000000000^{1000000000^{10)}} is 1000000000000^{(1000000000^{10})/2}