Solve frac{(3.5)^{3}+3^{4}*(5^{2})^{4}}{((-2.3)^2)^5*(5^3)^4}=

$$\frac { ( 3.5 ) ^ { 3 } + 3 ^ { 4 } \cdot ( 5 ^ { 2 } ) ^ { 4 } } { ( ( - 2.3 ) ^ { 2 } ) ^ { 5 } \cdot ( 5 ^ { 3 } ) ^ { 4 } } =$$

Evaluate

$$\frac{32400043904}{1035662780341225}\approx 0.000031284$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{3.5^{3}+3^{4}\times 5^{8}}{\left(\left(-2.3\right)^{2}\right)^{5}\times \left(5^{3}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{3.5^{3}+3^{4}\times 5^{8}}{\left(-2.3\right)^{10}\times \left(5^{3}\right)^{4}}$$

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

$$\frac{3.5^{3}+3^{4}\times 5^{8}}{\left(-2.3\right)^{10}\times 5^{12}}$$

Calculate 3.5 to the power of 3 and get 42.875.

$$\frac{42.875+3^{4}\times 5^{8}}{\left(-2.3\right)^{10}\times 5^{12}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{42.875+81\times 5^{8}}{\left(-2.3\right)^{10}\times 5^{12}}$$

Calculate 5 to the power of 8 and get 390625.

$$\frac{42.875+81\times 390625}{\left(-2.3\right)^{10}\times 5^{12}}$$

Multiply 81 and 390625 to get 31640625.

$$\frac{42.875+31640625}{\left(-2.3\right)^{10}\times 5^{12}}$$

Add 42.875 and 31640625 to get 31640667.875.

$$\frac{31640667.875}{\left(-2.3\right)^{10}\times 5^{12}}$$

Calculate -2.3 to the power of 10 and get 4142.6511213649.

$$\frac{31640667.875}{4142.6511213649\times 5^{12}}$$

Calculate 5 to the power of 12 and get 244140625.

$$\frac{31640667.875}{4142.6511213649\times 244140625}$$

Multiply 4142.6511213649 and 244140625 to get 1011389433926.9775390625.

$$\frac{31640667.875}{1011389433926.9775390625}$$

Expand \frac{31640667.875}{1011389433926.9775390625} by multiplying both numerator and the denominator by 10000000000.

$$\frac{316406678750000000}{10113894339269775390625}$$

Reduce the fraction \frac{316406678750000000}{10113894339269775390625} to lowest terms by extracting and canceling out 9765625.

$$\frac{32400043904}{1035662780341225}$$

Factor

$$\frac{253125343 \cdot 2 ^ {7}}{5 ^ {2} \cdot 23 ^ {10}} = 3.128435676072572 \times 10^{-5}$$