Solve (13)(7/9)^{-2}div(7/9)^-3-(1.9-2)^0-(-1/3)^-2div(-3)^-1

$$( 13 ) ( \frac { 7 } { 9 } ) ^ { - 2 } \div ( \frac { 7 } { 9 } ) ^ { - 3 } - ( 1.9 - 2 ) ^ { 0 } - ( - \frac { 1 } { 3 } ) ^ { - 2 } \div ( - 3 ) ^ { - 1 }$$

Evaluate

$$\frac{325}{9}\approx 36.111111111$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$13\times \left(\frac{7}{9}\right)^{1}-\left(1.9-2\right)^{0}-\frac{\left(-\frac{1}{3}\right)^{-2}}{\left(-3\right)^{-1}}$$

Subtract 2 from 1.9 to get -0.1.

$$13\times \left(\frac{7}{9}\right)^{1}-\left(-0.1\right)^{0}-\frac{\left(-\frac{1}{3}\right)^{-2}}{\left(-3\right)^{-1}}$$

Calculate -0.1 to the power of 0 and get 1.

$$13\times \left(\frac{7}{9}\right)^{1}-1-\frac{\left(-\frac{1}{3}\right)^{-2}}{\left(-3\right)^{-1}}$$

Calculate -\frac{1}{3} to the power of -2 and get 9.

$$13\times \left(\frac{7}{9}\right)^{1}-1-\frac{9}{\left(-3\right)^{-1}}$$

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

$$13\times \left(\frac{7}{9}\right)^{1}-1-\frac{9}{-\frac{1}{3}}$$

Divide 9 by -\frac{1}{3} by multiplying 9 by the reciprocal of -\frac{1}{3}.

$$13\times \left(\frac{7}{9}\right)^{1}-1-9\left(-3\right)$$

Multiply 9 and -3 to get -27.

$$13\times \left(\frac{7}{9}\right)^{1}-1-\left(-27\right)$$

The opposite of -27 is 27.

$$13\times \left(\frac{7}{9}\right)^{1}-1+27$$

Add -1 and 27 to get 26.

$$13\times \left(\frac{7}{9}\right)^{1}+26$$

Calculate \frac{7}{9} to the power of 1 and get \frac{7}{9}.

$$13\times \frac{7}{9}+26$$

Multiply 13 and \frac{7}{9} to get \frac{91}{9}.

$$\frac{91}{9}+26$$

Add \frac{91}{9} and 26 to get \frac{325}{9}.

$$\frac{325}{9}$$

Factor

$$\frac{13 \cdot 5 ^ {2}}{3 ^ {2}} = 36\frac{1}{9} = 36.111111111111114$$