Solve 8*3*5/1{left(3/7right)}^3{left(7/15right)}^7

$$\frac{ 8 \times 3 \times 5 }{ 1 } { \left( \frac{ 3 }{ 7 } \right) }^{ 3 } { \left( \frac{ 7 }{ 15 } \right) }^{ 7 }$$

Evaluate

$$\frac{19208}{421875}\approx 0.045530074$$

Solution Steps

Multiply 8 and 3 to get 24.

$$\frac{24\times 5}{1}\times \left(\frac{3}{7}\right)^{3}\times \left(\frac{7}{15}\right)^{7}$$

Multiply 24 and 5 to get 120.

$$\frac{120}{1}\times \left(\frac{3}{7}\right)^{3}\times \left(\frac{7}{15}\right)^{7}$$

Anything divided by one gives itself.

$$120\times \left(\frac{3}{7}\right)^{3}\times \left(\frac{7}{15}\right)^{7}$$

Calculate \frac{3}{7} to the power of 3 and get \frac{27}{343}.

$$120\times \frac{27}{343}\times \left(\frac{7}{15}\right)^{7}$$

Express 120\times \frac{27}{343} as a single fraction.

$$\frac{120\times 27}{343}\times \left(\frac{7}{15}\right)^{7}$$

Multiply 120 and 27 to get 3240.

$$\frac{3240}{343}\times \left(\frac{7}{15}\right)^{7}$$

Calculate \frac{7}{15} to the power of 7 and get \frac{823543}{170859375}.

$$\frac{3240}{343}\times \frac{823543}{170859375}$$

Multiply \frac{3240}{343} times \frac{823543}{170859375} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3240\times 823543}{343\times 170859375}$$

Do the multiplications in the fraction \frac{3240\times 823543}{343\times 170859375}.

$$\frac{2668279320}{58604765625}$$

Reduce the fraction \frac{2668279320}{58604765625} to lowest terms by extracting and canceling out 138915.

$$\frac{19208}{421875}$$

Factor

$$\frac{2 ^ {3} \cdot 7 ^ {4}}{3 ^ {3} \cdot 5 ^ {6}} = 0.04553007407407408$$