Solve frac{667*10^{-11}+6*10^24}{(64*10^3+3*64*10^5)^2}=

$$\frac { 667 \cdot 10 ^ { - 11 } + 6 \cdot 10 ^ { 24 } } { ( 64 \cdot 10 ^ { 3 } + 3 \cdot 64 \cdot 10 ^ { 5 } ) ^ { 2 } } =$$

Evaluate

$$\frac{600000000000000000000000000000000667}{37110169600000000000000000}\approx 16168074855.685919581$$

Solution Steps

Calculate 10 to the power of -11 and get \frac{1}{100000000000}.

$$\frac{667\times \frac{1}{100000000000}+6\times 10^{24}}{\left(64\times 10^{3}+3\times 64\times 10^{5}\right)^{2}}$$

Multiply 667 and \frac{1}{100000000000} to get \frac{667}{100000000000}.

$$\frac{\frac{667}{100000000000}+6\times 10^{24}}{\left(64\times 10^{3}+3\times 64\times 10^{5}\right)^{2}}$$

Calculate 10 to the power of 24 and get 1000000000000000000000000.

$$\frac{\frac{667}{100000000000}+6\times 1000000000000000000000000}{\left(64\times 10^{3}+3\times 64\times 10^{5}\right)^{2}}$$

Multiply 6 and 1000000000000000000000000 to get 6000000000000000000000000.

$$\frac{\frac{667}{100000000000}+6000000000000000000000000}{\left(64\times 10^{3}+3\times 64\times 10^{5}\right)^{2}}$$

Add \frac{667}{100000000000} and 6000000000000000000000000 to get \frac{600000000000000000000000000000000667}{100000000000}.

$$\frac{\frac{600000000000000000000000000000000667}{100000000000}}{\left(64\times 10^{3}+3\times 64\times 10^{5}\right)^{2}}$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{\frac{600000000000000000000000000000000667}{100000000000}}{\left(64\times 1000+3\times 64\times 10^{5}\right)^{2}}$$

Multiply 64 and 1000 to get 64000.

$$\frac{\frac{600000000000000000000000000000000667}{100000000000}}{\left(64000+3\times 64\times 10^{5}\right)^{2}}$$

Multiply 3 and 64 to get 192.

$$\frac{\frac{600000000000000000000000000000000667}{100000000000}}{\left(64000+192\times 10^{5}\right)^{2}}$$

Calculate 10 to the power of 5 and get 100000.

$$\frac{\frac{600000000000000000000000000000000667}{100000000000}}{\left(64000+192\times 100000\right)^{2}}$$

Multiply 192 and 100000 to get 19200000.

$$\frac{\frac{600000000000000000000000000000000667}{100000000000}}{\left(64000+19200000\right)^{2}}$$

Add 64000 and 19200000 to get 19264000.

$$\frac{\frac{600000000000000000000000000000000667}{100000000000}}{19264000^{2}}$$

Calculate 19264000 to the power of 2 and get 371101696000000.

$$\frac{\frac{600000000000000000000000000000000667}{100000000000}}{371101696000000}$$

Express \frac{\frac{600000000000000000000000000000000667}{100000000000}}{371101696000000} as a single fraction.

$$\frac{600000000000000000000000000000000667}{100000000000\times 371101696000000}$$

Multiply 100000000000 and 371101696000000 to get 37110169600000000000000000.

$$\frac{600000000000000000000000000000000667}{37110169600000000000000000}$$