Solve [(3/5)^-2*(3/3)^4]^3:(3/5)^4=

$$[ ( \frac { 3 } { 5 } ) ^ { - 2 } \cdot ( \frac { 3 } { 3 } ) ^ { 4 } ] ^ { 3 } : ( \frac { 3 } { 5 } ) ^ { 4 } =$$

Evaluate

$$\frac{9765625}{59049}\approx 165.381716879$$

Solution Steps

Divide 3 by 3 to get 1.

$$\frac{\left(\left(\frac{3}{5}\right)^{-2}\times 1^{4}\right)^{3}}{\left(\frac{3}{5}\right)^{4}}$$

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

$$\frac{\left(\frac{25}{9}\times 1^{4}\right)^{3}}{\left(\frac{3}{5}\right)^{4}}$$

Calculate 1 to the power of 4 and get 1.

$$\frac{\left(\frac{25}{9}\times 1\right)^{3}}{\left(\frac{3}{5}\right)^{4}}$$

Multiply \frac{25}{9} and 1 to get \frac{25}{9}.

$$\frac{\left(\frac{25}{9}\right)^{3}}{\left(\frac{3}{5}\right)^{4}}$$

Calculate \frac{25}{9} to the power of 3 and get \frac{15625}{729}.

$$\frac{\frac{15625}{729}}{\left(\frac{3}{5}\right)^{4}}$$

Calculate \frac{3}{5} to the power of 4 and get \frac{81}{625}.

$$\frac{\frac{15625}{729}}{\frac{81}{625}}$$

Divide \frac{15625}{729} by \frac{81}{625} by multiplying \frac{15625}{729} by the reciprocal of \frac{81}{625}.

$$\frac{15625}{729}\times \frac{625}{81}$$

Multiply \frac{15625}{729} and \frac{625}{81} to get \frac{9765625}{59049}.

$$\frac{9765625}{59049}$$

Factor

$$\frac{5 ^ {10}}{3 ^ {10}} = 165\frac{22540}{59049} = 165.38171687920203$$