Solve [(3/2)^{4}]^-0,5*(7/12)^0*0,1^-2:(0,81)^-0,5

$$[ ( \frac { 3 } { 2 } ) ^ { 4 } ] ^ { - 0,5 } \cdot ( \frac { 7 } { 12 } ) ^ { 0 } \cdot 0,1 ^ { - 2 } : ( 0,81 ) ^ { - 0,5 }$$

Evaluate

$$0$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and -0,5 to get -2.

$$\frac{\left(\frac{3}{2}\right)^{-2}\times \left(\frac{7}{12}\right)^{0}\times 0\times 1^{-2}}{0,81^{-0,5}}$$

Calculate \frac{3}{2} to the power of -2 and get \frac{4}{9}.

$$\frac{\frac{4}{9}\times \left(\frac{7}{12}\right)^{0}\times 0\times 1^{-2}}{0,81^{-0,5}}$$

Calculate \frac{7}{12} to the power of 0 and get 1.

$$\frac{\frac{4}{9}\times 1\times 0\times 1^{-2}}{0,81^{-0,5}}$$

Multiply \frac{4}{9} and 1 to get \frac{4}{9}.

$$\frac{\frac{4}{9}\times 0\times 1^{-2}}{0,81^{-0,5}}$$

Multiply \frac{4}{9} and 0 to get 0.

$$\frac{0\times 1^{-2}}{0,81^{-0,5}}$$

Calculate 1 to the power of -2 and get 1.

$$\frac{0\times 1}{0,81^{-0,5}}$$

Multiply 0 and 1 to get 0.

$$\frac{0}{0,81^{-0,5}}$$

Calculate 0,81 to the power of -0,5 and get \frac{10}{9}.

$$\frac{0}{\frac{10}{9}}$$

Zero divided by any non-zero number gives zero.

$$0$$

Factor

$$0$$