Solve 1/3pi[-64x^3/27+2(164^2/9)^4]

$$\frac { 1 } { 3 } \pi [ \frac { - 64 x ^ { 3 } } { 27 } + 2 ( \frac { 164 ^ { 2 } } { 9 } ) ^ { 4 } ]$$

Evaluate

$$\frac{64\pi \left(16353126869239808-243x^{3}\right)}{19683}$$

Short Solution Steps

Calculate 164 to the power of 2 and get 26896.

$$\frac{1}{3}\pi \left(\frac{-64x^{3}}{27}+2\times \left(\frac{26896}{9}\right)^{4}\right)$$

Calculate \frac{26896}{9} to the power of 4 and get \frac{523300059815673856}{6561}.

$$\frac{1}{3}\pi \left(\frac{-64x^{3}}{27}+2\times \frac{523300059815673856}{6561}\right)$$

Multiply 2 and \frac{523300059815673856}{6561} to get \frac{1046600119631347712}{6561}.

$$\frac{1}{3}\pi \left(\frac{-64x^{3}}{27}+\frac{1046600119631347712}{6561}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 27 and 6561 is 6561. Multiply \frac{-64x^{3}}{27} times \frac{243}{243}.

$$\frac{1}{3}\pi \left(\frac{243\left(-64\right)x^{3}}{6561}+\frac{1046600119631347712}{6561}\right)$$

Since \frac{243\left(-64\right)x^{3}}{6561} and \frac{1046600119631347712}{6561} have the same denominator, add them by adding their numerators.

$$\frac{1}{3}\pi \times \frac{243\left(-64\right)x^{3}+1046600119631347712}{6561}$$

Do the multiplications in 243\left(-64\right)x^{3}+1046600119631347712.

$$\frac{1}{3}\pi \times \frac{-15552x^{3}+1046600119631347712}{6561}$$

Multiply \frac{1}{3} times \frac{-15552x^{3}+1046600119631347712}{6561} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-15552x^{3}+1046600119631347712}{3\times 6561}\pi$$

Multiply 3 and 6561 to get 19683.

$$\frac{-15552x^{3}+1046600119631347712}{19683}\pi$$

Express \frac{-15552x^{3}+1046600119631347712}{19683}\pi as a single fraction.

$$\frac{\left(-15552x^{3}+1046600119631347712\right)\pi }{19683}$$

Use the distributive property to multiply -15552x^{3}+1046600119631347712 by \pi .

$$\frac{-15552x^{3}\pi +1046600119631347712\pi }{19683}$$

Expand

$$-\frac{64\pi x^{3}}{81}+\frac{1046600119631347712\pi }{19683}$$

Short Solution Steps

Calculate 164 to the power of 2 and get 26896.

$$\frac{1}{3}\pi \left(\frac{-64x^{3}}{27}+2\times \left(\frac{26896}{9}\right)^{4}\right)$$

Calculate \frac{26896}{9} to the power of 4 and get \frac{523300059815673856}{6561}.

$$\frac{1}{3}\pi \left(\frac{-64x^{3}}{27}+2\times \frac{523300059815673856}{6561}\right)$$

Multiply 2 and \frac{523300059815673856}{6561} to get \frac{1046600119631347712}{6561}.

$$\frac{1}{3}\pi \left(\frac{-64x^{3}}{27}+\frac{1046600119631347712}{6561}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 27 and 6561 is 6561. Multiply \frac{-64x^{3}}{27} times \frac{243}{243}.

$$\frac{1}{3}\pi \left(\frac{243\left(-64\right)x^{3}}{6561}+\frac{1046600119631347712}{6561}\right)$$

Since \frac{243\left(-64\right)x^{3}}{6561} and \frac{1046600119631347712}{6561} have the same denominator, add them by adding their numerators.

$$\frac{1}{3}\pi \times \frac{243\left(-64\right)x^{3}+1046600119631347712}{6561}$$

Do the multiplications in 243\left(-64\right)x^{3}+1046600119631347712.

$$\frac{1}{3}\pi \times \frac{-15552x^{3}+1046600119631347712}{6561}$$

Multiply \frac{1}{3} times \frac{-15552x^{3}+1046600119631347712}{6561} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-15552x^{3}+1046600119631347712}{3\times 6561}\pi$$

Multiply 3 and 6561 to get 19683.

$$\frac{-15552x^{3}+1046600119631347712}{19683}\pi$$

Express \frac{-15552x^{3}+1046600119631347712}{19683}\pi as a single fraction.

$$\frac{\left(-15552x^{3}+1046600119631347712\right)\pi }{19683}$$

Use the distributive property to multiply -15552x^{3}+1046600119631347712 by \pi .

$$\frac{-15552x^{3}\pi +1046600119631347712\pi }{19683}$$