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

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

Evaluate

$$32400$$

Solution Steps

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

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{8^{5}\times 3^{4}\times \left(\frac{5}{4}\right)^{2}}{2^{7}}$$

Calculate 8 to the power of 5 and get 32768.

$$\frac{32768\times 3^{4}\times \left(\frac{5}{4}\right)^{2}}{2^{7}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{32768\times 81\times \left(\frac{5}{4}\right)^{2}}{2^{7}}$$

Multiply 32768 and 81 to get 2654208.

$$\frac{2654208\times \left(\frac{5}{4}\right)^{2}}{2^{7}}$$

Calculate \frac{5}{4} to the power of 2 and get \frac{25}{16}.

$$\frac{2654208\times \frac{25}{16}}{2^{7}}$$

Multiply 2654208 and \frac{25}{16} to get 4147200.

$$\frac{4147200}{2^{7}}$$

Calculate 2 to the power of 7 and get 128.

$$\frac{4147200}{128}$$

Divide 4147200 by 128 to get 32400.

$$32400$$

Factor

$$2^{4}\times 3^{4}\times 5^{2}$$