Solve frac{(3^{2}*7)^{5}*(2^{4})^{2}}{(5^3*2)^-2*(2^3*3)^2}

$$\frac { ( 3 ^ { 2 } \times 7 ) ^ { 5 } \times ( 2 ^ { 4 } ) ^ { 2 } } { ( 5 ^ { 3 } \times 2 ) ^ { - 2 } \times ( 2 ^ { 3 } \times 3 ) ^ { 2 } }$$

Evaluate

$$27567681750000$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{\left(3^{2}\times 7\right)^{5}\times 2^{8}}{\left(5^{3}\times 2\right)^{-2}\times \left(2^{3}\times 3\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\left(9\times 7\right)^{5}\times 2^{8}}{\left(5^{3}\times 2\right)^{-2}\times \left(2^{3}\times 3\right)^{2}}$$

Multiply 9 and 7 to get 63.

$$\frac{63^{5}\times 2^{8}}{\left(5^{3}\times 2\right)^{-2}\times \left(2^{3}\times 3\right)^{2}}$$

Calculate 63 to the power of 5 and get 992436543.

$$\frac{992436543\times 2^{8}}{\left(5^{3}\times 2\right)^{-2}\times \left(2^{3}\times 3\right)^{2}}$$

Calculate 2 to the power of 8 and get 256.

$$\frac{992436543\times 256}{\left(5^{3}\times 2\right)^{-2}\times \left(2^{3}\times 3\right)^{2}}$$

Multiply 992436543 and 256 to get 254063755008.

$$\frac{254063755008}{\left(5^{3}\times 2\right)^{-2}\times \left(2^{3}\times 3\right)^{2}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{254063755008}{\left(125\times 2\right)^{-2}\times \left(2^{3}\times 3\right)^{2}}$$

Multiply 125 and 2 to get 250.

$$\frac{254063755008}{250^{-2}\times \left(2^{3}\times 3\right)^{2}}$$

Calculate 250 to the power of -2 and get \frac{1}{62500}.

$$\frac{254063755008}{\frac{1}{62500}\times \left(2^{3}\times 3\right)^{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{254063755008}{\frac{1}{62500}\times \left(8\times 3\right)^{2}}$$

Multiply 8 and 3 to get 24.

$$\frac{254063755008}{\frac{1}{62500}\times 24^{2}}$$

Calculate 24 to the power of 2 and get 576.

$$\frac{254063755008}{\frac{1}{62500}\times 576}$$

Multiply \frac{1}{62500} and 576 to get \frac{144}{15625}.

$$\frac{254063755008}{\frac{144}{15625}}$$

Divide 254063755008 by \frac{144}{15625} by multiplying 254063755008 by the reciprocal of \frac{144}{15625}.

$$254063755008\times \frac{15625}{144}$$

Multiply 254063755008 and \frac{15625}{144} to get 27567681750000.

$$27567681750000$$

Factor

$$2^{4}\times 3^{8}\times 5^{6}\times 7^{5}$$