Solve pi/4:a*a^{5}+(2a^3)^2+(-2a^2)^3

$$\frac { \pi } { 4 } : a \cdot a ^ { 5 } + ( 2 a ^ { 3 } ) ^ { 2 } + ( - 2 a ^ { 2 } ) ^ { 3 }$$

Evaluate

$$-4a^{6}+\frac{\pi a^{4}}{4}$$

Short Solution Steps

Express \frac{\frac{\pi }{4}}{a} as a single fraction.

$$\frac{\pi }{4a}a^{5}+\left(2a^{3}\right)^{2}+\left(-2a^{2}\right)^{3}$$

Express \frac{\pi }{4a}a^{5} as a single fraction.

$$\frac{\pi a^{5}}{4a}+\left(2a^{3}\right)^{2}+\left(-2a^{2}\right)^{3}$$

Cancel out a in both numerator and denominator.

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

Expand \left(2a^{3}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\pi a^{4}}{4}+2^{2}a^{6}+\left(-2a^{2}\right)^{3}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\pi a^{4}}{4}+4a^{6}+\left(-2a^{2}\right)^{3}$$

Expand \left(-2a^{2}\right)^{3}.

$$\frac{\pi a^{4}}{4}+4a^{6}+\left(-2\right)^{3}\left(a^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\pi a^{4}}{4}+4a^{6}+\left(-2\right)^{3}a^{6}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{\pi a^{4}}{4}+4a^{6}-8a^{6}$$

Combine 4a^{6} and -8a^{6} to get -4a^{6}.

$$\frac{\pi a^{4}}{4}-4a^{6}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -4a^{6} times \frac{4}{4}.

$$\frac{\pi a^{4}}{4}+\frac{4\left(-4\right)a^{6}}{4}$$

Since \frac{\pi a^{4}}{4} and \frac{4\left(-4\right)a^{6}}{4} have the same denominator, add them by adding their numerators.

$$\frac{\pi a^{4}+4\left(-4\right)a^{6}}{4}$$

Do the multiplications in \pi a^{4}+4\left(-4\right)a^{6}.

$$\frac{\pi a^{4}-16a^{6}}{4}$$

Expand

$$-4a^{6}+\frac{\pi a^{4}}{4}$$

Short Solution Steps

Express \frac{\frac{\pi }{4}}{a} as a single fraction.

$$\frac{\pi }{4a}a^{5}+\left(2a^{3}\right)^{2}+\left(-2a^{2}\right)^{3}$$

Express \frac{\pi }{4a}a^{5} as a single fraction.

$$\frac{\pi a^{5}}{4a}+\left(2a^{3}\right)^{2}+\left(-2a^{2}\right)^{3}$$

Cancel out a in both numerator and denominator.

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

Expand \left(2a^{3}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\pi a^{4}}{4}+2^{2}a^{6}+\left(-2a^{2}\right)^{3}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\pi a^{4}}{4}+4a^{6}+\left(-2a^{2}\right)^{3}$$

Expand \left(-2a^{2}\right)^{3}.

$$\frac{\pi a^{4}}{4}+4a^{6}+\left(-2\right)^{3}\left(a^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\pi a^{4}}{4}+4a^{6}+\left(-2\right)^{3}a^{6}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{\pi a^{4}}{4}+4a^{6}-8a^{6}$$

Combine 4a^{6} and -8a^{6} to get -4a^{6}.

$$\frac{\pi a^{4}}{4}-4a^{6}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -4a^{6} times \frac{4}{4}.

$$\frac{\pi a^{4}}{4}+\frac{4\left(-4\right)a^{6}}{4}$$

Since \frac{\pi a^{4}}{4} and \frac{4\left(-4\right)a^{6}}{4} have the same denominator, add them by adding their numerators.

$$\frac{\pi a^{4}+4\left(-4\right)a^{6}}{4}$$

Do the multiplications in \pi a^{4}+4\left(-4\right)a^{6}.

$$\frac{\pi a^{4}-16a^{6}}{4}$$