Solve frac{(10^{-5})^{-3}*(10^{-3})^2}{10^-4*10^-5*10^6}

$$\frac { ( 10 ^ { - 5 } ) ^ { - 3 } \times ( 10 ^ { - 3 } ) ^ { 2 } } { 10 ^ { - 4 } \times 10 ^ { - 5 } \times 10 ^ { 6 } }$$

Evaluate

$$1000000000000$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -5 and -3 to get 15.

$$\frac{10^{15}\times \left(10^{-3}\right)^{2}}{10^{-4}\times 10^{-5}\times 10^{6}}$$

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

$$\frac{10^{15}\times 10^{-6}}{10^{-4}\times 10^{-5}\times 10^{6}}$$

To multiply powers of the same base, add their exponents. Add 15 and -6 to get 9.

$$\frac{10^{9}}{10^{-4}\times 10^{-5}\times 10^{6}}$$

To multiply powers of the same base, add their exponents. Add -4 and -5 to get -9.

$$\frac{10^{9}}{10^{-9}\times 10^{6}}$$

To multiply powers of the same base, add their exponents. Add -9 and 6 to get -3.

$$\frac{10^{9}}{10^{-3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -3 from 9 to get 12.

$$10^{12}$$

Calculate 10 to the power of 12 and get 1000000000000.

$$1000000000000$$

Factor

$$2^{12}\times 5^{12}$$