Solve frac{(10^{3})^{2}div10^{3^{3}}}{(10^2)^3div10^2^3}

$$\frac { ( 10 ^ { 3 } ) ^ { 2 } \div 10 ^ { 3 ^ { 3 } } } { ( 10 ^ { 2 } ) ^ { 3 } \div 10 ^ { 2 ^ { 3 } } }$$

Evaluate

$$\frac{1}{10000000000000000000}= 10^{-19}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\frac{10^{6}}{10^{3^{3}}}}{\frac{\left(10^{2}\right)^{3}}{10^{2^{3}}}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\frac{10^{6}}{10^{3^{3}}}}{\frac{10^{6}}{10^{2^{3}}}}$$

Divide \frac{10^{6}}{10^{3^{3}}} by \frac{10^{6}}{10^{2^{3}}} by multiplying \frac{10^{6}}{10^{3^{3}}} by the reciprocal of \frac{10^{6}}{10^{2^{3}}}.

$$\frac{10^{6}\times 10^{2^{3}}}{10^{3^{3}}\times 10^{6}}$$

Cancel out 10^{6} in both numerator and denominator.

$$\frac{10^{2^{3}}}{10^{3^{3}}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{10^{8}}{10^{3^{3}}}$$

Calculate 10 to the power of 8 and get 100000000.

$$\frac{100000000}{10^{3^{3}}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{100000000}{10^{27}}$$

Calculate 10 to the power of 27 and get 1000000000000000000000000000.

$$\frac{100000000}{1000000000000000000000000000}$$

Reduce the fraction \frac{100000000}{1000000000000000000000000000} to lowest terms by extracting and canceling out 100000000.

$$\frac{1}{10000000000000000000}$$

Factor

$$\frac{1}{2 ^ {19} \cdot 5 ^ {19}} = 1 \times 10^{-19}$$