Solve (1/2*10^3*10*10*12^2)-(1/2*10^3*10*10*4^2)

$$( \frac{ 1 }{ 2 } \times { 10 }^{ 3 } \times 10 \times 10 \times { 12 }^{ 2 } )-( \frac{ 1 }{ 2 } \times { 10 }^{ 3 } \times 10 \times 10 \times { 4 }^{ 2 } )$$

Evaluate

$$6400000$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{1}{2}\times 10^{4}\times 10\times 12^{2}-\frac{1}{2}\times 10^{3}\times 10\times 10\times 4^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{1}{2}\times 10^{5}\times 12^{2}-\frac{1}{2}\times 10^{3}\times 10\times 10\times 4^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{1}{2}\times 10^{5}\times 12^{2}-\frac{1}{2}\times 10^{4}\times 10\times 4^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{1}{2}\times 10^{5}\times 12^{2}-\frac{1}{2}\times 10^{5}\times 4^{2}$$

Calculate 10 to the power of 5 and get 100000.

$$\frac{1}{2}\times 100000\times 12^{2}-\frac{1}{2}\times 10^{5}\times 4^{2}$$

Multiply \frac{1}{2} and 100000 to get \frac{100000}{2}.

$$\frac{100000}{2}\times 12^{2}-\frac{1}{2}\times 10^{5}\times 4^{2}$$

Divide 100000 by 2 to get 50000.

$$50000\times 12^{2}-\frac{1}{2}\times 10^{5}\times 4^{2}$$

Calculate 12 to the power of 2 and get 144.

$$50000\times 144-\frac{1}{2}\times 10^{5}\times 4^{2}$$

Multiply 50000 and 144 to get 7200000.

$$7200000-\frac{1}{2}\times 10^{5}\times 4^{2}$$

Calculate 10 to the power of 5 and get 100000.

$$7200000-\frac{1}{2}\times 100000\times 4^{2}$$

Multiply \frac{1}{2} and 100000 to get \frac{100000}{2}.

$$7200000-\frac{100000}{2}\times 4^{2}$$

Divide 100000 by 2 to get 50000.

$$7200000-50000\times 4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$7200000-50000\times 16$$

Multiply 50000 and 16 to get 800000.

$$7200000-800000$$

Subtract 800000 from 7200000 to get 6400000.

$$6400000$$

Factor

$$2^{11}\times 5^{5}$$