Solve [(3/5)^{2}]^5*(1/3)^-4*(3)^-2*(2)^-1

$$[ ( \frac { 3 } { 5 } ) ^ { 2 } ] ^ { 5 } \times ( \frac { 1 } { 3 } ) ^ { - 4 } \times ( 3 ) ^ { - 2 } \times ( 2 ) ^ { - 1 }$$

Evaluate

$$\frac{531441}{19531250}=0.027209779$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\left(\frac{3}{5}\right)^{10}\times \left(\frac{1}{3}\right)^{-4}\times 3^{-2}\times 2^{-1}$$

Calculate \frac{3}{5} to the power of 10 and get \frac{59049}{9765625}.

$$\frac{59049}{9765625}\times \left(\frac{1}{3}\right)^{-4}\times 3^{-2}\times 2^{-1}$$

Calculate \frac{1}{3} to the power of -4 and get 81.

$$\frac{59049}{9765625}\times 81\times 3^{-2}\times 2^{-1}$$

Multiply \frac{59049}{9765625} and 81 to get \frac{4782969}{9765625}.

$$\frac{4782969}{9765625}\times 3^{-2}\times 2^{-1}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{4782969}{9765625}\times \frac{1}{9}\times 2^{-1}$$

Multiply \frac{4782969}{9765625} and \frac{1}{9} to get \frac{531441}{9765625}.

$$\frac{531441}{9765625}\times 2^{-1}$$

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

$$\frac{531441}{9765625}\times \frac{1}{2}$$

Multiply \frac{531441}{9765625} and \frac{1}{2} to get \frac{531441}{19531250}.

$$\frac{531441}{19531250}$$

Factor

$$\frac{3 ^ {12}}{2 \cdot 5 ^ {10}} = 0.0272097792$$