Solve frac{sqrt{7^-4*11^4}}{49*121}

$$\frac { \sqrt { 7 ^ { - 4 } \times 11 ^ { 4 } } } { 49 \times 121 }$$

Evaluate

$$\frac{1}{2401}\approx 0.000416493$$

Solution Steps

Calculate 7 to the power of -4 and get \frac{1}{2401}.

$$\frac{\sqrt{\frac{1}{2401}\times 11^{4}}}{49\times 121}$$

Calculate 11 to the power of 4 and get 14641.

$$\frac{\sqrt{\frac{1}{2401}\times 14641}}{49\times 121}$$

Multiply \frac{1}{2401} and 14641 to get \frac{14641}{2401}.

$$\frac{\sqrt{\frac{14641}{2401}}}{49\times 121}$$

Rewrite the square root of the division \frac{14641}{2401} as the division of square roots \frac{\sqrt{14641}}{\sqrt{2401}}. Take the square root of both numerator and denominator.

$$\frac{\frac{121}{49}}{49\times 121}$$

Multiply 49 and 121 to get 5929.

$$\frac{\frac{121}{49}}{5929}$$

Express \frac{\frac{121}{49}}{5929} as a single fraction.

$$\frac{121}{49\times 5929}$$

Multiply 49 and 5929 to get 290521.

$$\frac{121}{290521}$$

Reduce the fraction \frac{121}{290521} to lowest terms by extracting and canceling out 121.

$$\frac{1}{2401}$$

Factor

$$\frac{1}{7 ^ {4}} = 0.00041649312786339027$$