Solve frac{(3^4)^frac{1{2}}}{27^-2*25}

$$\frac { ( 3 ^ { 4 } ) ^ { \frac { 1 } { 2 } } } { 27 ^ { - 2 } \times 25 }$$

Evaluate

$$\frac{6561}{25}=262.44$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and \frac{1}{2} to get 2.

$$\frac{3^{2}}{27^{-2}\times 25}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9}{27^{-2}\times 25}$$

Calculate 27 to the power of -2 and get \frac{1}{729}.

$$\frac{9}{\frac{1}{729}\times 25}$$

Multiply \frac{1}{729} and 25 to get \frac{25}{729}.

$$\frac{9}{\frac{25}{729}}$$

Divide 9 by \frac{25}{729} by multiplying 9 by the reciprocal of \frac{25}{729}.

$$9\times \frac{729}{25}$$

Multiply 9 and \frac{729}{25} to get \frac{6561}{25}.

$$\frac{6561}{25}$$

Factor

$$\frac{3 ^ {8}}{5 ^ {2}} = 262\frac{11}{25} = 262.44$$