Solve x(2*64)=(0.5*(4*64)*64)(64+64/3)+(0.5*4(64)*64)(2(64/3))

$$x(2 \times 64)=(0.5 \times (4 \times 64) \times 64)(64+ \frac{ 64 }{ 3 } )+(0.5 \times 4(64) \times 64)(2( \frac{ 64 }{ 3 } ))$$

Evaluate

$$1048576$$

Solution Steps

Multiply 0.5 and 4 to get 2.

$$2\times 64\times 64\left(64+\frac{64}{3}\right)+0.5\times 4\times 64\times 64\times 2\times \frac{64}{3}$$

Multiply 2 and 64 to get 128.

$$128\times 64\left(64+\frac{64}{3}\right)+0.5\times 4\times 64\times 64\times 2\times \frac{64}{3}$$

Multiply 128 and 64 to get 8192.

$$8192\left(64+\frac{64}{3}\right)+0.5\times 4\times 64\times 64\times 2\times \frac{64}{3}$$

Convert 64 to fraction \frac{192}{3}.

$$8192\left(\frac{192}{3}+\frac{64}{3}\right)+0.5\times 4\times 64\times 64\times 2\times \frac{64}{3}$$

Since \frac{192}{3} and \frac{64}{3} have the same denominator, add them by adding their numerators.

$$8192\times \frac{192+64}{3}+0.5\times 4\times 64\times 64\times 2\times \frac{64}{3}$$

Add 192 and 64 to get 256.

$$8192\times \frac{256}{3}+0.5\times 4\times 64\times 64\times 2\times \frac{64}{3}$$

Express 8192\times \frac{256}{3} as a single fraction.

$$\frac{8192\times 256}{3}+0.5\times 4\times 64\times 64\times 2\times \frac{64}{3}$$

Multiply 8192 and 256 to get 2097152.

$$\frac{2097152}{3}+0.5\times 4\times 64\times 64\times 2\times \frac{64}{3}$$

Multiply 0.5 and 4 to get 2.

$$\frac{2097152}{3}+2\times 64\times 64\times 2\times \frac{64}{3}$$

Multiply 2 and 64 to get 128.

$$\frac{2097152}{3}+128\times 64\times 2\times \frac{64}{3}$$

Multiply 128 and 64 to get 8192.

$$\frac{2097152}{3}+8192\times 2\times \frac{64}{3}$$

Multiply 8192 and 2 to get 16384.

$$\frac{2097152}{3}+16384\times \frac{64}{3}$$

Express 16384\times \frac{64}{3} as a single fraction.

$$\frac{2097152}{3}+\frac{16384\times 64}{3}$$

Multiply 16384 and 64 to get 1048576.

$$\frac{2097152}{3}+\frac{1048576}{3}$$

Since \frac{2097152}{3} and \frac{1048576}{3} have the same denominator, add them by adding their numerators.

$$\frac{2097152+1048576}{3}$$

Add 2097152 and 1048576 to get 3145728.

$$\frac{3145728}{3}$$

Divide 3145728 by 3 to get 1048576.

$$1048576$$

Factor

$$2^{20}$$