Solve (-8*10^{11})^{-2}*(-8*10^{11})^{-3}div[(4*10^5)^4*(2*10^-6)^+1]

$$( - 8 \times 10 ^ { 11 } ) ^ { - 2 } \times ( - 8 \times 10 ^ { 11 } ) ^ { - 3 } \div [ ( 4 \times 10 ^ { 5 } ) ^ { 4 } \times ( 2 \times 10 ^ { - 6 } ) ^ { + 1 } ]$$

Evaluate

$$-\frac{1}{16777216000000000000000000000000000000000000000000000000000000000000000000000}=-5.960464478 \cdot 10^{-77}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -2 and -3 to get -5.

$$\frac{\left(-8\times 10^{11}\right)^{-5}}{\left(4\times 10^{5}\right)^{4}\times \left(2\times 10^{-6}\right)^{1}}$$

Calculate 10 to the power of 11 and get 100000000000.

$$\frac{\left(-8\times 100000000000\right)^{-5}}{\left(4\times 10^{5}\right)^{4}\times \left(2\times 10^{-6}\right)^{1}}$$

Multiply -8 and 100000000000 to get -800000000000.

$$\frac{\left(-800000000000\right)^{-5}}{\left(4\times 10^{5}\right)^{4}\times \left(2\times 10^{-6}\right)^{1}}$$

Calculate -800000000000 to the power of -5 and get -\frac{1}{327680000000000000000000000000000000000000000000000000000000}.

$$\frac{-\frac{1}{327680000000000000000000000000000000000000000000000000000000}}{\left(4\times 10^{5}\right)^{4}\times \left(2\times 10^{-6}\right)^{1}}$$

Calculate 10 to the power of 5 and get 100000.

$$\frac{-\frac{1}{327680000000000000000000000000000000000000000000000000000000}}{\left(4\times 100000\right)^{4}\times \left(2\times 10^{-6}\right)^{1}}$$

Multiply 4 and 100000 to get 400000.

$$\frac{-\frac{1}{327680000000000000000000000000000000000000000000000000000000}}{400000^{4}\times \left(2\times 10^{-6}\right)^{1}}$$

Calculate 400000 to the power of 4 and get 25600000000000000000000.

$$\frac{-\frac{1}{327680000000000000000000000000000000000000000000000000000000}}{25600000000000000000000\times \left(2\times 10^{-6}\right)^{1}}$$

Calculate 10 to the power of -6 and get \frac{1}{1000000}.

$$\frac{-\frac{1}{327680000000000000000000000000000000000000000000000000000000}}{25600000000000000000000\times \left(2\times \frac{1}{1000000}\right)^{1}}$$

Multiply 2 and \frac{1}{1000000} to get \frac{1}{500000}.

$$\frac{-\frac{1}{327680000000000000000000000000000000000000000000000000000000}}{25600000000000000000000\times \left(\frac{1}{500000}\right)^{1}}$$

Calculate \frac{1}{500000} to the power of 1 and get \frac{1}{500000}.

$$\frac{-\frac{1}{327680000000000000000000000000000000000000000000000000000000}}{25600000000000000000000\times \frac{1}{500000}}$$

Multiply 25600000000000000000000 and \frac{1}{500000} to get 51200000000000000.

$$\frac{-\frac{1}{327680000000000000000000000000000000000000000000000000000000}}{51200000000000000}$$

Express \frac{-\frac{1}{327680000000000000000000000000000000000000000000000000000000}}{51200000000000000} as a single fraction.

$$\frac{-1}{327680000000000000000000000000000000000000000000000000000000\times 51200000000000000}$$

Multiply 327680000000000000000000000000000000000000000000000000000000 and 51200000000000000 to get 16777216000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{-1}{16777216000000000000000000000000000000000000000000000000000000000000000000000}$$

Fraction \frac{-1}{16777216000000000000000000000000000000000000000000000000000000000000000000000} can be rewritten as -\frac{1}{16777216000000000000000000000000000000000000000000000000000000000000000000000} by extracting the negative sign.

$$-\frac{1}{16777216000000000000000000000000000000000000000000000000000000000000000000000}$$

Factor

$$-\frac{1}{16777216000000000000000000000000000000000000000000000000000000000000000000000} = -5.9604644775390625 \times 10^{-77}$$