Solve 1/21/3sqrt{81^423}

$$\frac { 1 } { 2 } \frac { 1 } { 3 } \sqrt { 81 ^ { 42 } 3 }$$

Evaluate

$$\frac{3990838394187339929534246675572349035227\sqrt{3}}{2}\approx 3.456167432 \cdot 10^{39}$$

Solution Steps

Multiply \frac{1}{2} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 1}{2\times 3}\sqrt{81^{42}\times 3}$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 3}.

$$\frac{1}{6}\sqrt{81^{42}\times 3}$$

Calculate 81 to the power of 42 and get 143341119796678074027577337316118932770382415738332565090012937927177499182473761.

$$\frac{1}{6}\sqrt{143341119796678074027577337316118932770382415738332565090012937927177499182473761\times 3}$$

Multiply 143341119796678074027577337316118932770382415738332565090012937927177499182473761 and 3 to get 430023359390034222082732011948356798311147247214997695270038813781532497547421283.

$$\frac{1}{6}\sqrt{430023359390034222082732011948356798311147247214997695270038813781532497547421283}$$

Factor 430023359390034222082732011948356798311147247214997695270038813781532497547421283=11972515182562019788602740026717047105681^{2}\times 3. Rewrite the square root of the product \sqrt{11972515182562019788602740026717047105681^{2}\times 3} as the product of square roots \sqrt{11972515182562019788602740026717047105681^{2}}\sqrt{3}. Take the square root of 11972515182562019788602740026717047105681^{2}.

$$\frac{1}{6}\times 11972515182562019788602740026717047105681\sqrt{3}$$

Multiply \frac{1}{6} and 11972515182562019788602740026717047105681 to get \frac{11972515182562019788602740026717047105681}{6}.

$$\frac{11972515182562019788602740026717047105681}{6}\sqrt{3}$$

Reduce the fraction \frac{11972515182562019788602740026717047105681}{6} to lowest terms by extracting and canceling out 3.

$$\frac{3990838394187339929534246675572349035227}{2}\sqrt{3}$$