Solve 10^-4410^-30.2/frac{3{8}left(1.310^-2right)^4}

$$\frac{ { 10 }^{ -4 } 4 { 10 }^{ -3 } 0.2 }{ \frac{ 3 }{ 8 } { \left(1.3 { 10 }^{ -2 } \right) }^{ 4 } }$$

Evaluate

$$\frac{640000}{85683}\approx 7.469392995$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -4 and -3 to get -7.

$$\frac{10^{-7}\times 4\times 0.2}{\frac{3}{8}\times \left(1.3\times 10^{-2}\right)^{4}}$$

Calculate 10 to the power of -7 and get \frac{1}{10000000}.

$$\frac{\frac{1}{10000000}\times 4\times 0.2}{\frac{3}{8}\times \left(1.3\times 10^{-2}\right)^{4}}$$

Multiply \frac{1}{10000000} and 4 to get \frac{1}{2500000}.

$$\frac{\frac{1}{2500000}\times 0.2}{\frac{3}{8}\times \left(1.3\times 10^{-2}\right)^{4}}$$

Multiply \frac{1}{2500000} and 0.2 to get \frac{1}{12500000}.

$$\frac{\frac{1}{12500000}}{\frac{3}{8}\times \left(1.3\times 10^{-2}\right)^{4}}$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{\frac{1}{12500000}}{\frac{3}{8}\times \left(1.3\times \frac{1}{100}\right)^{4}}$$

Multiply 1.3 and \frac{1}{100} to get \frac{13}{1000}.

$$\frac{\frac{1}{12500000}}{\frac{3}{8}\times \left(\frac{13}{1000}\right)^{4}}$$

Calculate \frac{13}{1000} to the power of 4 and get \frac{28561}{1000000000000}.

$$\frac{\frac{1}{12500000}}{\frac{3}{8}\times \frac{28561}{1000000000000}}$$

Multiply \frac{3}{8} and \frac{28561}{1000000000000} to get \frac{85683}{8000000000000}.

$$\frac{\frac{1}{12500000}}{\frac{85683}{8000000000000}}$$

Divide \frac{1}{12500000} by \frac{85683}{8000000000000} by multiplying \frac{1}{12500000} by the reciprocal of \frac{85683}{8000000000000}.

$$\frac{1}{12500000}\times \frac{8000000000000}{85683}$$

Multiply \frac{1}{12500000} and \frac{8000000000000}{85683} to get \frac{640000}{85683}.

$$\frac{640000}{85683}$$

Factor

$$\frac{2 ^ {10} \cdot 5 ^ {4}}{3 \cdot 13 ^ {4}} = 7\frac{40219}{85683} = 7.469392995109882$$