Solve (-3)^2div21/4*(-2/3)^2+4-2^2*(-1/3)

$$( - 3 ) ^ { 2 } \div 2 \frac { 1 } { 4 } \times ( - \frac { 2 } { 3 } ) ^ { 2 } + 4 - 2 ^ { 2 } \times ( - \frac { 1 } { 3 } )$$

Evaluate

$$\frac{64}{9}\approx 7.111111111$$

Solution Steps

Calculate -3 to the power of 2 and get 9.

$$\frac{9}{\frac{2\times 4+1}{4}}\left(-\frac{2}{3}\right)^{2}+4-2^{2}\left(-\frac{1}{3}\right)$$

Multiply 2 and 4 to get 8.

$$\frac{9}{\frac{8+1}{4}}\left(-\frac{2}{3}\right)^{2}+4-2^{2}\left(-\frac{1}{3}\right)$$

Add 8 and 1 to get 9.

$$\frac{9}{\frac{9}{4}}\left(-\frac{2}{3}\right)^{2}+4-2^{2}\left(-\frac{1}{3}\right)$$

Divide 9 by \frac{9}{4} by multiplying 9 by the reciprocal of \frac{9}{4}.

$$9\times \frac{4}{9}\left(-\frac{2}{3}\right)^{2}+4-2^{2}\left(-\frac{1}{3}\right)$$

Cancel out 9 and 9.

$$4\left(-\frac{2}{3}\right)^{2}+4-2^{2}\left(-\frac{1}{3}\right)$$

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

$$4\times \frac{4}{9}+4-2^{2}\left(-\frac{1}{3}\right)$$

Express 4\times \frac{4}{9} as a single fraction.

$$\frac{4\times 4}{9}+4-2^{2}\left(-\frac{1}{3}\right)$$

Multiply 4 and 4 to get 16.

$$\frac{16}{9}+4-2^{2}\left(-\frac{1}{3}\right)$$

Convert 4 to fraction \frac{36}{9}.

$$\frac{16}{9}+\frac{36}{9}-2^{2}\left(-\frac{1}{3}\right)$$

Since \frac{16}{9} and \frac{36}{9} have the same denominator, add them by adding their numerators.

$$\frac{16+36}{9}-2^{2}\left(-\frac{1}{3}\right)$$

Add 16 and 36 to get 52.

$$\frac{52}{9}-2^{2}\left(-\frac{1}{3}\right)$$

Calculate 2 to the power of 2 and get 4.

$$\frac{52}{9}-4\left(-\frac{1}{3}\right)$$

Express 4\left(-\frac{1}{3}\right) as a single fraction.

$$\frac{52}{9}-\frac{4\left(-1\right)}{3}$$

Multiply 4 and -1 to get -4.

$$\frac{52}{9}-\frac{-4}{3}$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$\frac{52}{9}-\left(-\frac{4}{3}\right)$$

The opposite of -\frac{4}{3} is \frac{4}{3}.

$$\frac{52}{9}+\frac{4}{3}$$

Least common multiple of 9 and 3 is 9. Convert \frac{52}{9} and \frac{4}{3} to fractions with denominator 9.

$$\frac{52}{9}+\frac{12}{9}$$

Since \frac{52}{9} and \frac{12}{9} have the same denominator, add them by adding their numerators.

$$\frac{52+12}{9}$$

Add 52 and 12 to get 64.

$$\frac{64}{9}$$

Factor

$$\frac{2 ^ {6}}{3 ^ {2}} = 7\frac{1}{9} = 7.111111111111111$$