Solve (7/34/59/5frac{9/3)^{-5}}{(4^2*3^75^2frac{6}{5})^-7}

$$\frac { ( \frac { 7 } { 3 } \frac { 4 } { 5 } \frac { 9 } { 5 } \frac { 9 } { 3 } ) ^ { - 5 } } { ( 4 ^ { 2 } \cdot 3 ^ { 7 } 5 ^ { 2 } \frac { 6 } { 5 } ) ^ { - 7 } }$$

Evaluate

$$\frac{226891215863104028055782400000000000000000}{16807}\approx 1.34998046 \cdot 10^{37}$$

Solution Steps

Multiply \frac{7}{3} and \frac{4}{5} to get \frac{28}{15}.

$$\frac{\left(\frac{28}{15}\times \frac{9}{5}\times \frac{9}{3}\right)^{-5}}{\left(4^{2}\times 3^{7}\times 5^{2}\times \frac{6}{5}\right)^{-7}}$$

Multiply \frac{28}{15} and \frac{9}{5} to get \frac{84}{25}.

$$\frac{\left(\frac{84}{25}\times \frac{9}{3}\right)^{-5}}{\left(4^{2}\times 3^{7}\times 5^{2}\times \frac{6}{5}\right)^{-7}}$$

Divide 9 by 3 to get 3.

$$\frac{\left(\frac{84}{25}\times 3\right)^{-5}}{\left(4^{2}\times 3^{7}\times 5^{2}\times \frac{6}{5}\right)^{-7}}$$

Multiply \frac{84}{25} and 3 to get \frac{252}{25}.

$$\frac{\left(\frac{252}{25}\right)^{-5}}{\left(4^{2}\times 3^{7}\times 5^{2}\times \frac{6}{5}\right)^{-7}}$$

Calculate \frac{252}{25} to the power of -5 and get \frac{9765625}{1016255020032}.

$$\frac{\frac{9765625}{1016255020032}}{\left(4^{2}\times 3^{7}\times 5^{2}\times \frac{6}{5}\right)^{-7}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{\frac{9765625}{1016255020032}}{\left(16\times 3^{7}\times 5^{2}\times \frac{6}{5}\right)^{-7}}$$

Calculate 3 to the power of 7 and get 2187.

$$\frac{\frac{9765625}{1016255020032}}{\left(16\times 2187\times 5^{2}\times \frac{6}{5}\right)^{-7}}$$

Multiply 16 and 2187 to get 34992.

$$\frac{\frac{9765625}{1016255020032}}{\left(34992\times 5^{2}\times \frac{6}{5}\right)^{-7}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\frac{9765625}{1016255020032}}{\left(34992\times 25\times \frac{6}{5}\right)^{-7}}$$

Multiply 34992 and 25 to get 874800.

$$\frac{\frac{9765625}{1016255020032}}{\left(874800\times \frac{6}{5}\right)^{-7}}$$

Multiply 874800 and \frac{6}{5} to get 1049760.

$$\frac{\frac{9765625}{1016255020032}}{1049760^{-7}}$$

Calculate 1049760 to the power of -7 and get \frac{1}{1404850605182201862833139345008885760000000}.

$$\frac{\frac{9765625}{1016255020032}}{\frac{1}{1404850605182201862833139345008885760000000}}$$

Divide \frac{9765625}{1016255020032} by \frac{1}{1404850605182201862833139345008885760000000} by multiplying \frac{9765625}{1016255020032} by the reciprocal of \frac{1}{1404850605182201862833139345008885760000000}.

$$\frac{9765625}{1016255020032}\times 1404850605182201862833139345008885760000000$$

Multiply \frac{9765625}{1016255020032} and 1404850605182201862833139345008885760000000 to get \frac{226891215863104028055782400000000000000000}{16807}.

$$\frac{226891215863104028055782400000000000000000}{16807}$$

Factor

$$\frac{2 ^ {25} \cdot 3 ^ {46} \cdot 5 ^ {17}}{7 ^ {5}} = 1.3499804597078837 \times 10^{37}\frac{2570}{16807} = 1.3499804597078837 \times 10^{37}$$