Solve frac{(10^{2})^3:10^5}{10^2:70^6}

$$\frac { ( 10 ^ { 2 } ) ^ { 3 } : 10 ^ { 5 } } { 10 ^ { 2 } : 70 ^ { 6 } }$$

Evaluate

$$11764900000$$

Solution Steps

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

$$\frac{\frac{10^{6}}{10^{5}}}{\frac{10^{2}}{70^{6}}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 6 to get 1.

$$\frac{10^{1}}{\frac{10^{2}}{70^{6}}}$$

Calculate 10 to the power of 1 and get 10.

$$\frac{10}{\frac{10^{2}}{70^{6}}}$$

Calculate 10 to the power of 2 and get 100.

$$\frac{10}{\frac{100}{70^{6}}}$$

Calculate 70 to the power of 6 and get 117649000000.

$$\frac{10}{\frac{100}{117649000000}}$$

Reduce the fraction \frac{100}{117649000000} to lowest terms by extracting and canceling out 100.

$$\frac{10}{\frac{1}{1176490000}}$$

Divide 10 by \frac{1}{1176490000} by multiplying 10 by the reciprocal of \frac{1}{1176490000}.

$$10\times 1176490000$$

Multiply 10 and 1176490000 to get 11764900000.

$$11764900000$$

Factor

$$2^{5}\times 5^{5}\times 7^{6}$$