Solve 3/8*sqrt{frac{7}9^4}*8/7

$$\frac { 3 } { 8 } \cdot \sqrt { \frac { 7 } { 9 } ^ { 4 } } \times \frac { 8 } { 7 }$$

Evaluate

$$\frac{7}{27}\approx 0.259259259$$

Solution Steps

Calculate \frac{7}{9} to the power of 4 and get \frac{2401}{6561}.

$$\frac{3}{8}\sqrt{\frac{2401}{6561}}\times \frac{8}{7}$$

Rewrite the square root of the division \frac{2401}{6561} as the division of square roots \frac{\sqrt{2401}}{\sqrt{6561}}. Take the square root of both numerator and denominator.

$$\frac{3}{8}\times \frac{49}{81}\times \frac{8}{7}$$

Multiply \frac{3}{8} times \frac{49}{81} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 49}{8\times 81}\times \frac{8}{7}$$

Do the multiplications in the fraction \frac{3\times 49}{8\times 81}.

$$\frac{147}{648}\times \frac{8}{7}$$

Reduce the fraction \frac{147}{648} to lowest terms by extracting and canceling out 3.

$$\frac{49}{216}\times \frac{8}{7}$$

Multiply \frac{49}{216} times \frac{8}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{49\times 8}{216\times 7}$$

Do the multiplications in the fraction \frac{49\times 8}{216\times 7}.

$$\frac{392}{1512}$$

Reduce the fraction \frac{392}{1512} to lowest terms by extracting and canceling out 56.

$$\frac{7}{27}$$

Factor

$$\frac{7}{3 ^ {3}} = 0.25925925925925924$$