Solve (-3)^0+(1-2/5)^-2div7/9*7/5-(-1/6)^-2

$$( - 3 ) ^ { 0 } + ( 1 - \frac { 2 } { 5 } ) ^ { - 2 } \div \frac { 7 } { 9 } \times \frac { 7 } { 5 } - ( - \frac { 1 } { 6 } ) ^ { - 2 }$$

Evaluate

$$-30$$

Solution Steps

Calculate -3 to the power of 0 and get 1.

$$1+\frac{\left(1-\frac{2}{5}\right)^{-2}}{\frac{7}{9}}\times \frac{7}{5}-\left(-\frac{1}{6}\right)^{-2}$$

Subtract \frac{2}{5} from 1 to get \frac{3}{5}.

$$1+\frac{\left(\frac{3}{5}\right)^{-2}}{\frac{7}{9}}\times \frac{7}{5}-\left(-\frac{1}{6}\right)^{-2}$$

Calculate \frac{3}{5} to the power of -2 and get \frac{25}{9}.

$$1+\frac{\frac{25}{9}}{\frac{7}{9}}\times \frac{7}{5}-\left(-\frac{1}{6}\right)^{-2}$$

Divide \frac{25}{9} by \frac{7}{9} by multiplying \frac{25}{9} by the reciprocal of \frac{7}{9}.

$$1+\frac{25}{9}\times \frac{9}{7}\times \frac{7}{5}-\left(-\frac{1}{6}\right)^{-2}$$

Multiply \frac{25}{9} and \frac{9}{7} to get \frac{25}{7}.

$$1+\frac{25}{7}\times \frac{7}{5}-\left(-\frac{1}{6}\right)^{-2}$$

Multiply \frac{25}{7} and \frac{7}{5} to get 5.

$$1+5-\left(-\frac{1}{6}\right)^{-2}$$

Add 1 and 5 to get 6.

$$6-\left(-\frac{1}{6}\right)^{-2}$$

Calculate -\frac{1}{6} to the power of -2 and get 36.

$$6-36$$

Subtract 36 from 6 to get -30.

$$-30$$

Factor

$$-30$$