Solve (2^4*3^-6*5^2)^-1/2=

$$( 2 ^ { 4 } \cdot 3 ^ { - 6 } \cdot 5 ^ { 2 } ) ^ { - 1 / 2 } =$$

Evaluate

$$\frac{27}{20}=1.35$$

Solution Steps

Calculate 2 to the power of 4 and get 16.

$$\left(16\times 3^{-6}\times 5^{2}\right)^{-\frac{1}{2}}$$

Calculate 3 to the power of -6 and get \frac{1}{729}.

$$\left(16\times \frac{1}{729}\times 5^{2}\right)^{-\frac{1}{2}}$$

Multiply 16 and \frac{1}{729} to get \frac{16}{729}.

$$\left(\frac{16}{729}\times 5^{2}\right)^{-\frac{1}{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\left(\frac{16}{729}\times 25\right)^{-\frac{1}{2}}$$

Multiply \frac{16}{729} and 25 to get \frac{400}{729}.

$$\left(\frac{400}{729}\right)^{-\frac{1}{2}}$$

Calculate \frac{400}{729} to the power of -\frac{1}{2} and get \frac{27}{20}.

$$\frac{27}{20}$$

Factor

$$\frac{3 ^ {3}}{2 ^ {2} \cdot 5} = 1\frac{7}{20} = 1.35$$