Solve 5^47^52^9/84^9{5^2}

$$\frac{ { 5 }^{ 4 } { 7 }^{ 5 } { 2 }^{ 9 } }{ 8 { 4 }^{ 9 } { 5 }^{ 2 } }$$

Evaluate

$$\frac{420175}{4096}=102.581787109$$

Solution Steps

Cancel out 5^{2} in both numerator and denominator.

$$\frac{2^{9}\times 5^{2}\times 7^{5}}{8\times 4^{9}}$$

Calculate 2 to the power of 9 and get 512.

$$\frac{512\times 5^{2}\times 7^{5}}{8\times 4^{9}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{512\times 25\times 7^{5}}{8\times 4^{9}}$$

Multiply 512 and 25 to get 12800.

$$\frac{12800\times 7^{5}}{8\times 4^{9}}$$

Calculate 7 to the power of 5 and get 16807.

$$\frac{12800\times 16807}{8\times 4^{9}}$$

Multiply 12800 and 16807 to get 215129600.

$$\frac{215129600}{8\times 4^{9}}$$

Calculate 4 to the power of 9 and get 262144.

$$\frac{215129600}{8\times 262144}$$

Multiply 8 and 262144 to get 2097152.

$$\frac{215129600}{2097152}$$

Reduce the fraction \frac{215129600}{2097152} to lowest terms by extracting and canceling out 512.

$$\frac{420175}{4096}$$

Factor

$$\frac{5 ^ {2} \cdot 7 ^ {5}}{2 ^ {12}} = 102\frac{2383}{4096} = 102.581787109375$$