Solve {left(3/5right)}^80.2^-3{left(25/27right)}^49^2

$${ \left( \frac{ 3 }{ 5 } \right) }^{ 8 } { 0.2 }^{ -3 } { \left( \frac{ 25 }{ 27 } \right) }^{ 4 } { 9 }^{ 2 }$$

Evaluate

$$125$$

Solution Steps

Calculate \frac{3}{5} to the power of 8 and get \frac{6561}{390625}.

$$\frac{6561}{390625}\times 0.2^{-3}\times \left(\frac{25}{27}\right)^{4}\times 9^{2}$$

Calculate 0.2 to the power of -3 and get 125.

$$\frac{6561}{390625}\times 125\times \left(\frac{25}{27}\right)^{4}\times 9^{2}$$

Multiply \frac{6561}{390625} and 125 to get \frac{6561}{3125}.

$$\frac{6561}{3125}\times \left(\frac{25}{27}\right)^{4}\times 9^{2}$$

Calculate \frac{25}{27} to the power of 4 and get \frac{390625}{531441}.

$$\frac{6561}{3125}\times \frac{390625}{531441}\times 9^{2}$$

Multiply \frac{6561}{3125} and \frac{390625}{531441} to get \frac{125}{81}.

$$\frac{125}{81}\times 9^{2}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{125}{81}\times 81$$

Multiply \frac{125}{81} and 81 to get 125.

$$125$$

Factor

$$5^{3}$$