Solve (11/2)^{2}+2*11/2a^5+(8a)^2+(8a^2)^2=

$$( 1 \frac { 1 } { 2 } ) ^ { 2 } + 2 \cdot 1 \frac { 1 } { 2 } a ^ { 5 } + ( 8 a ) ^ { 2 } + ( 8 a ^ { 2 } ) ^ { 2 } =$$

Evaluate

$$3a^{5}+64a^{4}+64a^{2}+\frac{9}{4}$$

Solution Steps

Multiply 1 and 2 to get 2.

$$\left(\frac{2+1}{2}\right)^{2}+2\times \frac{1\times 2+1}{2}a^{5}+\left(8a\right)^{2}+\left(8a^{2}\right)^{2}$$

Add 2 and 1 to get 3.

$$\left(\frac{3}{2}\right)^{2}+2\times \frac{1\times 2+1}{2}a^{5}+\left(8a\right)^{2}+\left(8a^{2}\right)^{2}$$

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

$$\frac{9}{4}+2\times \frac{1\times 2+1}{2}a^{5}+\left(8a\right)^{2}+\left(8a^{2}\right)^{2}$$

Multiply 1 and 2 to get 2.

$$\frac{9}{4}+2\times \frac{2+1}{2}a^{5}+\left(8a\right)^{2}+\left(8a^{2}\right)^{2}$$

Add 2 and 1 to get 3.

$$\frac{9}{4}+2\times \frac{3}{2}a^{5}+\left(8a\right)^{2}+\left(8a^{2}\right)^{2}$$

Multiply 2 and \frac{3}{2} to get 3.

$$\frac{9}{4}+3a^{5}+\left(8a\right)^{2}+\left(8a^{2}\right)^{2}$$

Expand \left(8a\right)^{2}.

$$\frac{9}{4}+3a^{5}+8^{2}a^{2}+\left(8a^{2}\right)^{2}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{9}{4}+3a^{5}+64a^{2}+\left(8a^{2}\right)^{2}$$

Expand \left(8a^{2}\right)^{2}.

$$\frac{9}{4}+3a^{5}+64a^{2}+8^{2}\left(a^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{9}{4}+3a^{5}+64a^{2}+8^{2}a^{4}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{9}{4}+3a^{5}+64a^{2}+64a^{4}$$

Expand

$$3a^{5}+64a^{4}+64a^{2}+\frac{9}{4}$$

Solution Steps

Multiply 1 and 2 to get 2.

$$\left(\frac{2+1}{2}\right)^{2}+2\times \frac{1\times 2+1}{2}a^{5}+\left(8a\right)^{2}+\left(8a^{2}\right)^{2}$$

Add 2 and 1 to get 3.

$$\left(\frac{3}{2}\right)^{2}+2\times \frac{1\times 2+1}{2}a^{5}+\left(8a\right)^{2}+\left(8a^{2}\right)^{2}$$

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

$$\frac{9}{4}+2\times \frac{1\times 2+1}{2}a^{5}+\left(8a\right)^{2}+\left(8a^{2}\right)^{2}$$

Multiply 1 and 2 to get 2.

$$\frac{9}{4}+2\times \frac{2+1}{2}a^{5}+\left(8a\right)^{2}+\left(8a^{2}\right)^{2}$$

Add 2 and 1 to get 3.

$$\frac{9}{4}+2\times \frac{3}{2}a^{5}+\left(8a\right)^{2}+\left(8a^{2}\right)^{2}$$

Multiply 2 and \frac{3}{2} to get 3.

$$\frac{9}{4}+3a^{5}+\left(8a\right)^{2}+\left(8a^{2}\right)^{2}$$

Expand \left(8a\right)^{2}.

$$\frac{9}{4}+3a^{5}+8^{2}a^{2}+\left(8a^{2}\right)^{2}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{9}{4}+3a^{5}+64a^{2}+\left(8a^{2}\right)^{2}$$

Expand \left(8a^{2}\right)^{2}.

$$\frac{9}{4}+3a^{5}+64a^{2}+8^{2}\left(a^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{9}{4}+3a^{5}+64a^{2}+8^{2}a^{4}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{9}{4}+3a^{5}+64a^{2}+64a^{4}$$