Solve 10-7(3)^3(-1/3)^2-3(3^2)(-1/3)+9(-1/3)^2+2(3)

$$10 - 7 ( 3 ) ^ { 3 } ( - \frac { 1 } { 3 } ) ^ { 2 } - 3 ( 3 ^ { 2 } ) ( - \frac { 1 } { 3 } ) + 9 ( - \frac { 1 } { 3 } ) ^ { 2 } + 2 ( 3 )$$

Evaluate

$$5$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$10-7\times 3^{3}\left(-\frac{1}{3}\right)^{2}-3^{3}\left(-\frac{1}{3}\right)+9\left(-\frac{1}{3}\right)^{2}+2\times 3$$

Calculate 3 to the power of 3 and get 27.

$$10-7\times 27\left(-\frac{1}{3}\right)^{2}-3^{3}\left(-\frac{1}{3}\right)+9\left(-\frac{1}{3}\right)^{2}+2\times 3$$

Multiply 7 and 27 to get 189.

$$10-189\left(-\frac{1}{3}\right)^{2}-3^{3}\left(-\frac{1}{3}\right)+9\left(-\frac{1}{3}\right)^{2}+2\times 3$$

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

$$10-189\times \frac{1}{9}-3^{3}\left(-\frac{1}{3}\right)+9\left(-\frac{1}{3}\right)^{2}+2\times 3$$

Multiply 189 and \frac{1}{9} to get \frac{189}{9}.

$$10-\frac{189}{9}-3^{3}\left(-\frac{1}{3}\right)+9\left(-\frac{1}{3}\right)^{2}+2\times 3$$

Divide 189 by 9 to get 21.

$$10-21-3^{3}\left(-\frac{1}{3}\right)+9\left(-\frac{1}{3}\right)^{2}+2\times 3$$

Subtract 21 from 10 to get -11.

$$-11-3^{3}\left(-\frac{1}{3}\right)+9\left(-\frac{1}{3}\right)^{2}+2\times 3$$

Calculate 3 to the power of 3 and get 27.

$$-11-27\left(-\frac{1}{3}\right)+9\left(-\frac{1}{3}\right)^{2}+2\times 3$$

Express 27\left(-\frac{1}{3}\right) as a single fraction.

$$-11-\frac{27\left(-1\right)}{3}+9\left(-\frac{1}{3}\right)^{2}+2\times 3$$

Multiply 27 and -1 to get -27.

$$-11-\frac{-27}{3}+9\left(-\frac{1}{3}\right)^{2}+2\times 3$$

Divide -27 by 3 to get -9.

$$-11-\left(-9\right)+9\left(-\frac{1}{3}\right)^{2}+2\times 3$$

The opposite of -9 is 9.

$$-11+9+9\left(-\frac{1}{3}\right)^{2}+2\times 3$$

Add -11 and 9 to get -2.

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

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

$$-2+9\times \frac{1}{9}+2\times 3$$

Cancel out 9 and 9.

$$-2+1+2\times 3$$

Add -2 and 1 to get -1.

$$-1+2\times 3$$

Multiply 2 and 3 to get 6.

$$-1+6$$

Add -1 and 6 to get 5.

$$5$$

Factor

$$5$$