Solve 1/2*5*10^5*30^2-1/2*5*10^5*10^2

$$\frac{ 1 }{ 2 } \times 5 \times { 10 }^{ 5 } \times { 30 }^{ 2 } - \frac{ 1 }{ 2 } \times 5 \times { 10 }^{ 5 } \times { 10 }^{ 2 }$$

Evaluate

$$200000000$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{1}{2}\times 5\times 10^{5}\times 30^{2}-\frac{1}{2}\times 5\times 10^{7}$$

Multiply \frac{1}{2} and 5 to get \frac{5}{2}.

$$\frac{5}{2}\times 10^{5}\times 30^{2}-\frac{1}{2}\times 5\times 10^{7}$$

Calculate 10 to the power of 5 and get 100000.

$$\frac{5}{2}\times 100000\times 30^{2}-\frac{1}{2}\times 5\times 10^{7}$$

Express \frac{5}{2}\times 100000 as a single fraction.

$$\frac{5\times 100000}{2}\times 30^{2}-\frac{1}{2}\times 5\times 10^{7}$$

Multiply 5 and 100000 to get 500000.

$$\frac{500000}{2}\times 30^{2}-\frac{1}{2}\times 5\times 10^{7}$$

Divide 500000 by 2 to get 250000.

$$250000\times 30^{2}-\frac{1}{2}\times 5\times 10^{7}$$

Calculate 30 to the power of 2 and get 900.

$$250000\times 900-\frac{1}{2}\times 5\times 10^{7}$$

Multiply 250000 and 900 to get 225000000.

$$225000000-\frac{1}{2}\times 5\times 10^{7}$$

Multiply \frac{1}{2} and 5 to get \frac{5}{2}.

$$225000000-\frac{5}{2}\times 10^{7}$$

Calculate 10 to the power of 7 and get 10000000.

$$225000000-\frac{5}{2}\times 10000000$$

Express \frac{5}{2}\times 10000000 as a single fraction.

$$225000000-\frac{5\times 10000000}{2}$$

Multiply 5 and 10000000 to get 50000000.

$$225000000-\frac{50000000}{2}$$

Divide 50000000 by 2 to get 25000000.

$$225000000-25000000$$

Subtract 25000000 from 225000000 to get 200000000.

$$200000000$$

Factor

$$2^{9}\times 5^{8}$$