Solve [frac{(5*8^{3})^{2}*(5*8)^{4}}{8^2*5^2*8^3}]^2

$$[ \frac { ( 5 \times 8 ^ { 3 } ) ^ { 2 } \times ( 5 \times 8 ) ^ { 4 } } { 8 ^ { 2 } \times 5 ^ { 2 } \times 8 ^ { 3 } } ] ^ { 2 }$$

Evaluate

$$419430400000000$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\left(\frac{\left(5\times 8^{3}\right)^{2}\times \left(5\times 8\right)^{4}}{8^{5}\times 5^{2}}\right)^{2}$$

Calculate 8 to the power of 3 and get 512.

$$\left(\frac{\left(5\times 512\right)^{2}\times \left(5\times 8\right)^{4}}{8^{5}\times 5^{2}}\right)^{2}$$

Multiply 5 and 512 to get 2560.

$$\left(\frac{2560^{2}\times \left(5\times 8\right)^{4}}{8^{5}\times 5^{2}}\right)^{2}$$

Calculate 2560 to the power of 2 and get 6553600.

$$\left(\frac{6553600\times \left(5\times 8\right)^{4}}{8^{5}\times 5^{2}}\right)^{2}$$

Multiply 5 and 8 to get 40.

$$\left(\frac{6553600\times 40^{4}}{8^{5}\times 5^{2}}\right)^{2}$$

Calculate 40 to the power of 4 and get 2560000.

$$\left(\frac{6553600\times 2560000}{8^{5}\times 5^{2}}\right)^{2}$$

Multiply 6553600 and 2560000 to get 16777216000000.

$$\left(\frac{16777216000000}{8^{5}\times 5^{2}}\right)^{2}$$

Calculate 8 to the power of 5 and get 32768.

$$\left(\frac{16777216000000}{32768\times 5^{2}}\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$\left(\frac{16777216000000}{32768\times 25}\right)^{2}$$

Multiply 32768 and 25 to get 819200.

$$\left(\frac{16777216000000}{819200}\right)^{2}$$

Divide 16777216000000 by 819200 to get 20480000.

$$20480000^{2}$$

Calculate 20480000 to the power of 2 and get 419430400000000.

$$419430400000000$$

Factor

$$2^{30}\times 5^{8}$$