Solve [1/(0.02)(0.03)^-1]^2

$$[ \frac { 1 } { ( 0.02 ) ( 0.03 ) ^ { - 1 } } ] ^ { 2 }$$

Evaluate

$$2.25$$

Solution Steps

Calculate 0.03 to the power of -1 and get \frac{100}{3}.

$$\left(\frac{1}{0.02\times \frac{100}{3}}\right)^{2}$$

Multiply 0.02 and \frac{100}{3} to get \frac{2}{3}.

$$\left(\frac{1}{\frac{2}{3}}\right)^{2}$$

To raise \frac{1}{\frac{2}{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{2}}{\frac{2}{3}^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{1}{\frac{2}{3}^{2}}$$

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

$$\frac{1}{\frac{4}{9}}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {2}} = 2\frac{1}{4} = 2.25$$