Solve frac{9^-1*27^-2*sqrt{9^4}}{(1/9)^2}

$$\frac { 9 ^ { - 1 } \cdot 27 ^ { - 2 } \cdot \sqrt { 9 ^ { 4 } } } { ( \frac { 1 } { 9 } ) ^ { 2 } }$$

Evaluate

$$1$$

Solution Steps

Calculate 9 to the power of -1 and get \frac{1}{9}.

$$\frac{\frac{1}{9}\times 27^{-2}\sqrt{9^{4}}}{\left(\frac{1}{9}\right)^{2}}$$

Calculate 27 to the power of -2 and get \frac{1}{729}.

$$\frac{\frac{1}{9}\times \frac{1}{729}\sqrt{9^{4}}}{\left(\frac{1}{9}\right)^{2}}$$

Multiply \frac{1}{9} and \frac{1}{729} to get \frac{1}{6561}.

$$\frac{\frac{1}{6561}\sqrt{9^{4}}}{\left(\frac{1}{9}\right)^{2}}$$

Calculate 9 to the power of 4 and get 6561.

$$\frac{\frac{1}{6561}\sqrt{6561}}{\left(\frac{1}{9}\right)^{2}}$$

Calculate the square root of 6561 and get 81.

$$\frac{\frac{1}{6561}\times 81}{\left(\frac{1}{9}\right)^{2}}$$

Multiply \frac{1}{6561} and 81 to get \frac{1}{81}.

$$\frac{\frac{1}{81}}{\left(\frac{1}{9}\right)^{2}}$$

Calculate \frac{1}{9} to the power of 2 and get \frac{1}{81}.

$$\frac{\frac{1}{81}}{\frac{1}{81}}$$

Divide \frac{1}{81} by \frac{1}{81} to get 1.

$$1$$

Factor

$$1$$