Solve 1/4(8/3)^3-(8/3)^2+6

$$\frac { 1 } { 4 } ( \frac { 8 } { 3 } ) ^ { 3 } - ( \frac { 8 } { 3 } ) ^ { 2 } + 6$$

Evaluate

$$\frac{98}{27}\approx 3.62962963$$

Solution Steps

Calculate \frac{8}{3} to the power of 3 and get \frac{512}{27}.

$$\frac{1}{4}\times \frac{512}{27}-\left(\frac{8}{3}\right)^{2}+6$$

Multiply \frac{1}{4} times \frac{512}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 512}{4\times 27}-\left(\frac{8}{3}\right)^{2}+6$$

Do the multiplications in the fraction \frac{1\times 512}{4\times 27}.

$$\frac{512}{108}-\left(\frac{8}{3}\right)^{2}+6$$

Reduce the fraction \frac{512}{108} to lowest terms by extracting and canceling out 4.

$$\frac{128}{27}-\left(\frac{8}{3}\right)^{2}+6$$

Calculate \frac{8}{3} to the power of 2 and get \frac{64}{9}.

$$\frac{128}{27}-\frac{64}{9}+6$$

Least common multiple of 27 and 9 is 27. Convert \frac{128}{27} and \frac{64}{9} to fractions with denominator 27.

$$\frac{128}{27}-\frac{192}{27}+6$$

Since \frac{128}{27} and \frac{192}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{128-192}{27}+6$$

Subtract 192 from 128 to get -64.

$$-\frac{64}{27}+6$$

Convert 6 to fraction \frac{162}{27}.

$$-\frac{64}{27}+\frac{162}{27}$$

Since -\frac{64}{27} and \frac{162}{27} have the same denominator, add them by adding their numerators.

$$\frac{-64+162}{27}$$

Add -64 and 162 to get 98.

$$\frac{98}{27}$$

Factor

$$\frac{2 \cdot 7 ^ {2}}{3 ^ {3}} = 3\frac{17}{27} = 3.6296296296296298$$