Solve ((3/8)^{2})^{-4}*(8/3)^2*3^2div5^2*(3/5)^-2

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

Evaluate

$$\frac{1073741824}{59049}\approx 18183.912073024$$

Solution Steps

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

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

Calculate \frac{3}{8} to the power of -8 and get \frac{16777216}{6561}.

$$\frac{\frac{16777216}{6561}\times \left(\frac{8}{3}\right)^{2}\times 3^{2}}{5^{2}}\times \left(\frac{3}{5}\right)^{-2}$$

Calculate \frac{8}{3} to the power of 2 and get \frac{64}{9}.

$$\frac{\frac{16777216}{6561}\times \frac{64}{9}\times 3^{2}}{5^{2}}\times \left(\frac{3}{5}\right)^{-2}$$

Multiply \frac{16777216}{6561} and \frac{64}{9} to get \frac{1073741824}{59049}.

$$\frac{\frac{1073741824}{59049}\times 3^{2}}{5^{2}}\times \left(\frac{3}{5}\right)^{-2}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\frac{1073741824}{59049}\times 9}{5^{2}}\times \left(\frac{3}{5}\right)^{-2}$$

Multiply \frac{1073741824}{59049} and 9 to get \frac{1073741824}{6561}.

$$\frac{\frac{1073741824}{6561}}{5^{2}}\times \left(\frac{3}{5}\right)^{-2}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\frac{1073741824}{6561}}{25}\times \left(\frac{3}{5}\right)^{-2}$$

Express \frac{\frac{1073741824}{6561}}{25} as a single fraction.

$$\frac{1073741824}{6561\times 25}\times \left(\frac{3}{5}\right)^{-2}$$

Multiply 6561 and 25 to get 164025.

$$\frac{1073741824}{164025}\times \left(\frac{3}{5}\right)^{-2}$$

Calculate \frac{3}{5} to the power of -2 and get \frac{25}{9}.

$$\frac{1073741824}{164025}\times \frac{25}{9}$$

Multiply \frac{1073741824}{164025} and \frac{25}{9} to get \frac{1073741824}{59049}.

$$\frac{1073741824}{59049}$$

Factor

$$\frac{2 ^ {30}}{3 ^ {10}} = 18183\frac{53857}{59049} = 18183.912073024097$$