Solve 2x-1/3x2/3+2/3*frac{2}3^2*1/3-frac{1}{9}*frac{23}{3}

$$2 x - \frac { 1 } { 3 } x \frac { 2 } { 3 } + \frac { 2 } { 3 } \times \frac { 2 } { 3 } ^ { 2 } \times \frac { 1 } { 3 } - \frac { 1 } { 9 } \times \frac { 23 } { 3 }$$

Evaluate

$$\frac{16x}{9}-\frac{61}{81}$$

Solution Steps

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

$$2x-\frac{1}{3}x\times \frac{2}{3}+\left(\frac{2}{3}\right)^{3}\times \frac{1}{3}-\frac{1}{9}\times \frac{23}{3}$$

Multiply \frac{1}{3} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$2x-\frac{1\times 2}{3\times 3}x+\left(\frac{2}{3}\right)^{3}\times \frac{1}{3}-\frac{1}{9}\times \frac{23}{3}$$

Do the multiplications in the fraction \frac{1\times 2}{3\times 3}.

$$2x-\frac{2}{9}x+\left(\frac{2}{3}\right)^{3}\times \frac{1}{3}-\frac{1}{9}\times \frac{23}{3}$$

Combine 2x and -\frac{2}{9}x to get \frac{16}{9}x.

$$\frac{16}{9}x+\left(\frac{2}{3}\right)^{3}\times \frac{1}{3}-\frac{1}{9}\times \frac{23}{3}$$

Calculate \frac{2}{3} to the power of 3 and get \frac{8}{27}.

$$\frac{16}{9}x+\frac{8}{27}\times \frac{1}{3}-\frac{1}{9}\times \frac{23}{3}$$

Multiply \frac{8}{27} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16}{9}x+\frac{8\times 1}{27\times 3}-\frac{1}{9}\times \frac{23}{3}$$

Do the multiplications in the fraction \frac{8\times 1}{27\times 3}.

$$\frac{16}{9}x+\frac{8}{81}-\frac{1}{9}\times \frac{23}{3}$$

Multiply \frac{1}{9} times \frac{23}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16}{9}x+\frac{8}{81}-\frac{1\times 23}{9\times 3}$$

Do the multiplications in the fraction \frac{1\times 23}{9\times 3}.

$$\frac{16}{9}x+\frac{8}{81}-\frac{23}{27}$$

Least common multiple of 81 and 27 is 81. Convert \frac{8}{81} and \frac{23}{27} to fractions with denominator 81.

$$\frac{16}{9}x+\frac{8}{81}-\frac{69}{81}$$

Since \frac{8}{81} and \frac{69}{81} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16}{9}x+\frac{8-69}{81}$$

Subtract 69 from 8 to get -61.

$$\frac{16}{9}x-\frac{61}{81}$$

Factor

$$\frac{144x-61}{81}$$

Solution Steps

Factor out \frac{1}{81}.

$$\frac{144x-61}{81}$$

Consider 162x-18x+8-69. Multiply and combine like terms.

$$144x-61$$

Rewrite the complete factored expression.

$$\frac{144x-61}{81}$$