Solve frac{2.4*(10^{-3})^4*10^10+0.76*10^-2}{10^4}

$$\frac { 2.4 \times ( 10 ^ { - 3 } ) ^ { 4 } \times 10 ^ { 10 } + 0.76 \times 10 ^ { - 2 } } { 10 ^ { 4 } }$$

Evaluate

$$0.00000316$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -3 and 4 to get -12.

$$\frac{2.4\times 10^{-12}\times 10^{10}+0.76\times 10^{-2}}{10^{4}}$$

To multiply powers of the same base, add their exponents. Add -12 and 10 to get -2.

$$\frac{2.4\times 10^{-2}+0.76\times 10^{-2}}{10^{4}}$$

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

$$\frac{2.4\times \frac{1}{100}+0.76\times 10^{-2}}{10^{4}}$$

Multiply 2.4 and \frac{1}{100} to get \frac{3}{125}.

$$\frac{\frac{3}{125}+0.76\times 10^{-2}}{10^{4}}$$

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

$$\frac{\frac{3}{125}+0.76\times \frac{1}{100}}{10^{4}}$$

Multiply 0.76 and \frac{1}{100} to get \frac{19}{2500}.

$$\frac{\frac{3}{125}+\frac{19}{2500}}{10^{4}}$$

Add \frac{3}{125} and \frac{19}{2500} to get \frac{79}{2500}.

$$\frac{\frac{79}{2500}}{10^{4}}$$

Calculate 10 to the power of 4 and get 10000.

$$\frac{\frac{79}{2500}}{10000}$$

Express \frac{\frac{79}{2500}}{10000} as a single fraction.

$$\frac{79}{2500\times 10000}$$

Multiply 2500 and 10000 to get 25000000.

$$\frac{79}{25000000}$$

Factor

$$\frac{79}{2 ^ {6} \cdot 5 ^ {8}} = 3.16 \times 10^{-6}$$