Solve 9/frac{frac{frac{frac{frac{frac{frac{frac{frac{frac{frac{frac{frac{frac{frac{9{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}

$$\frac { 9 } { \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ 9 }{ 9 } }{ 9 } }{ 9 } }{ 9 } }{ 9 } }{ 9 } }{ 9 } }{ 9 } }{ 9 } }{ 9 } }{ 9 } }{ 9 } }{ 9 } }{ 9 } }{ 9 } }$$

Evaluate

$$205891132094649$$

Solution Steps

Divide 9 by 9 to get 1.

$$\frac{9}{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}$$

Divide 9 by \frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9} by multiplying 9 by the reciprocal of \frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}.

$$\frac{9\times 9}{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}$$

Multiply 9 and 9 to get 81.

$$\frac{81}{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}$$

Express \frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9} as a single fraction.

$$\frac{81}{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9\times 9}}$$

Express \frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9} as a single fraction.

$$\frac{81}{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9\times 9}}{9\times 9}}$$

Express \frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9} as a single fraction.

$$\frac{81}{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{9}}{9}}{9}}{9}}{9}}{9}}{9}}{9\times 9}}{9\times 9}}{9\times 9}}$$

Express \frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{9}}{9}}{9}}{9}}{9}}{9}}{9} as a single fraction.

$$\frac{81}{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{9}}{9}}{9}}{9}}{9}}{9\times 9}}{9\times 9}}{9\times 9}}{9\times 9}}$$

Express \frac{\frac{\frac{\frac{\frac{1}{9}}{9}}{9}}{9}}{9} as a single fraction.

$$\frac{81}{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{9}}{9}}{9}}{9\times 9}}{9\times 9}}{9\times 9}}{9\times 9}}{9\times 9}}$$

Express \frac{\frac{\frac{1}{9}}{9}}{9} as a single fraction.

$$\frac{81}{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{9}}{9\times 9}}{9\times 9}}{9\times 9}}{9\times 9}}{9\times 9}}{9\times 9}}$$

Multiply 9 and 9 to get 81.

$$\frac{81}{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{9}}{81}}{9\times 9}}{9\times 9}}{9\times 9}}{9\times 9}}{9\times 9}}$$

Express \frac{\frac{1}{9}}{81} as a single fraction.

$$\frac{81}{\frac{\frac{\frac{\frac{\frac{\frac{1}{9\times 81}}{9\times 9}}{9\times 9}}{9\times 9}}{9\times 9}}{9\times 9}}$$

Multiply 9 and 81 to get 729.

$$\frac{81}{\frac{\frac{\frac{\frac{\frac{\frac{1}{729}}{9\times 9}}{9\times 9}}{9\times 9}}{9\times 9}}{9\times 9}}$$

Multiply 9 and 9 to get 81.

$$\frac{81}{\frac{\frac{\frac{\frac{\frac{\frac{1}{729}}{81}}{9\times 9}}{9\times 9}}{9\times 9}}{9\times 9}}$$

Express \frac{\frac{1}{729}}{81} as a single fraction.

$$\frac{81}{\frac{\frac{\frac{\frac{\frac{1}{729\times 81}}{9\times 9}}{9\times 9}}{9\times 9}}{9\times 9}}$$

Multiply 729 and 81 to get 59049.

$$\frac{81}{\frac{\frac{\frac{\frac{\frac{1}{59049}}{9\times 9}}{9\times 9}}{9\times 9}}{9\times 9}}$$

Multiply 9 and 9 to get 81.

$$\frac{81}{\frac{\frac{\frac{\frac{\frac{1}{59049}}{81}}{9\times 9}}{9\times 9}}{9\times 9}}$$

Express \frac{\frac{1}{59049}}{81} as a single fraction.

$$\frac{81}{\frac{\frac{\frac{\frac{1}{59049\times 81}}{9\times 9}}{9\times 9}}{9\times 9}}$$

Multiply 59049 and 81 to get 4782969.

$$\frac{81}{\frac{\frac{\frac{\frac{1}{4782969}}{9\times 9}}{9\times 9}}{9\times 9}}$$

Multiply 9 and 9 to get 81.

$$\frac{81}{\frac{\frac{\frac{\frac{1}{4782969}}{81}}{9\times 9}}{9\times 9}}$$

Express \frac{\frac{1}{4782969}}{81} as a single fraction.

$$\frac{81}{\frac{\frac{\frac{1}{4782969\times 81}}{9\times 9}}{9\times 9}}$$

Multiply 4782969 and 81 to get 387420489.

$$\frac{81}{\frac{\frac{\frac{1}{387420489}}{9\times 9}}{9\times 9}}$$

Multiply 9 and 9 to get 81.

$$\frac{81}{\frac{\frac{\frac{1}{387420489}}{81}}{9\times 9}}$$

Express \frac{\frac{1}{387420489}}{81} as a single fraction.

$$\frac{81}{\frac{\frac{1}{387420489\times 81}}{9\times 9}}$$

Multiply 387420489 and 81 to get 31381059609.

$$\frac{81}{\frac{\frac{1}{31381059609}}{9\times 9}}$$

Multiply 9 and 9 to get 81.

$$\frac{81}{\frac{\frac{1}{31381059609}}{81}}$$

Express \frac{\frac{1}{31381059609}}{81} as a single fraction.

$$\frac{81}{\frac{1}{31381059609\times 81}}$$

Multiply 31381059609 and 81 to get 2541865828329.

$$\frac{81}{\frac{1}{2541865828329}}$$

Divide 81 by \frac{1}{2541865828329} by multiplying 81 by the reciprocal of \frac{1}{2541865828329}.

$$81\times 2541865828329$$

Multiply 81 and 2541865828329 to get 205891132094649.

$$205891132094649$$

Factor

$$3^{30}$$