Solve 27^1frac{1{3}}*sqrt{1/9}div81^-frac{1{4}}

$$27 ^ { 1 \frac { 1 } { 3 } } \times \sqrt { \frac { 1 } { 9 } } \div 81 ^ { - \frac { 1 } { 4 } }$$

Evaluate

$$81$$

Solution Steps

Multiply 1 and 3 to get 3.

$$\frac{27^{\frac{3+1}{3}}\sqrt{\frac{1}{9}}}{81^{-\frac{1}{4}}}$$

Add 3 and 1 to get 4.

$$\frac{27^{\frac{4}{3}}\sqrt{\frac{1}{9}}}{81^{-\frac{1}{4}}}$$

Calculate 27 to the power of \frac{4}{3} and get 81.

$$\frac{81\sqrt{\frac{1}{9}}}{81^{-\frac{1}{4}}}$$

Rewrite the square root of the division \frac{1}{9} as the division of square roots \frac{\sqrt{1}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{81\times \frac{1}{3}}{81^{-\frac{1}{4}}}$$

Multiply 81 and \frac{1}{3} to get 27.

$$\frac{27}{81^{-\frac{1}{4}}}$$

Calculate 81 to the power of -\frac{1}{4} and get \frac{1}{3}.

$$\frac{27}{\frac{1}{3}}$$

Divide 27 by \frac{1}{3} by multiplying 27 by the reciprocal of \frac{1}{3}.

$$27\times 3$$

Multiply 27 and 3 to get 81.

$$81$$

Factor

$$3^{4}$$