Solve frac{(10^{2})^{9}*10^{-2}*10^3^2}{5^8*2^8}

$$\frac { ( 10 ^ { 2 } ) ^ { 9 } \cdot 10 ^ { - 2 } \times 10 ^ { 3 ^ { 2 } } } { 5 ^ { 8 } \cdot 2 ^ { 8 } }$$

Evaluate

$$100000000000000000$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 9 to get 18.

$$\frac{10^{18}\times 10^{-2}\times 10^{3^{2}}}{5^{8}\times 2^{8}}$$

To multiply powers of the same base, add their exponents. Add 18 and -2 to get 16.

$$\frac{10^{16}\times 10^{3^{2}}}{5^{8}\times 2^{8}}$$

Calculate 10 to the power of 16 and get 10000000000000000.

$$\frac{10000000000000000\times 10^{3^{2}}}{5^{8}\times 2^{8}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{10000000000000000\times 10^{9}}{5^{8}\times 2^{8}}$$

Calculate 10 to the power of 9 and get 1000000000.

$$\frac{10000000000000000\times 1000000000}{5^{8}\times 2^{8}}$$

Multiply 10000000000000000 and 1000000000 to get 10000000000000000000000000.

$$\frac{10000000000000000000000000}{5^{8}\times 2^{8}}$$

Calculate 5 to the power of 8 and get 390625.

$$\frac{10000000000000000000000000}{390625\times 2^{8}}$$

Calculate 2 to the power of 8 and get 256.

$$\frac{10000000000000000000000000}{390625\times 256}$$

Multiply 390625 and 256 to get 100000000.

$$\frac{10000000000000000000000000}{100000000}$$

Divide 10000000000000000000000000 by 100000000 to get 100000000000000000.

$$100000000000000000$$

Factor

$$2^{17}\times 5^{17}$$