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

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

Evaluate

$$\frac{6928538878797465155441400478424217075046875000000000000000000}{16807}\approx 4.122412613 \cdot 10^{56}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 6 to get 13.

$$\frac{\left(\frac{7}{3}\times \frac{4}{5}\times \frac{9}{5}\times \frac{9}{3}\right)^{-5}}{\left(4^{2}\times 3^{13}\times 5^{2}\right)^{-7}}$$

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

$$\frac{\left(\frac{28}{15}\times \frac{9}{5}\times \frac{9}{3}\right)^{-5}}{\left(4^{2}\times 3^{13}\times 5^{2}\right)^{-7}}$$

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

$$\frac{\left(\frac{84}{25}\times \frac{9}{3}\right)^{-5}}{\left(4^{2}\times 3^{13}\times 5^{2}\right)^{-7}}$$

Divide 9 by 3 to get 3.

$$\frac{\left(\frac{84}{25}\times 3\right)^{-5}}{\left(4^{2}\times 3^{13}\times 5^{2}\right)^{-7}}$$

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

$$\frac{\left(\frac{252}{25}\right)^{-5}}{\left(4^{2}\times 3^{13}\times 5^{2}\right)^{-7}}$$

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

$$\frac{\frac{9765625}{1016255020032}}{\left(4^{2}\times 3^{13}\times 5^{2}\right)^{-7}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{\frac{9765625}{1016255020032}}{\left(16\times 3^{13}\times 5^{2}\right)^{-7}}$$

Calculate 3 to the power of 13 and get 1594323.

$$\frac{\frac{9765625}{1016255020032}}{\left(16\times 1594323\times 5^{2}\right)^{-7}}$$

Multiply 16 and 1594323 to get 25509168.

$$\frac{\frac{9765625}{1016255020032}}{\left(25509168\times 5^{2}\right)^{-7}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\frac{9765625}{1016255020032}}{\left(25509168\times 25\right)^{-7}}$$

Multiply 25509168 and 25 to get 637729200.

$$\frac{\frac{9765625}{1016255020032}}{637729200^{-7}}$$

Calculate 637729200 to the power of -7 and get \frac{1}{42899686529864724115741396891124010221771730124800000000000000}.

$$\frac{\frac{9765625}{1016255020032}}{\frac{1}{42899686529864724115741396891124010221771730124800000000000000}}$$

Divide \frac{9765625}{1016255020032} by \frac{1}{42899686529864724115741396891124010221771730124800000000000000} by multiplying \frac{9765625}{1016255020032} by the reciprocal of \frac{1}{42899686529864724115741396891124010221771730124800000000000000}.

$$\frac{9765625}{1016255020032}\times 42899686529864724115741396891124010221771730124800000000000000$$

Multiply \frac{9765625}{1016255020032} and 42899686529864724115741396891124010221771730124800000000000000 to get \frac{6928538878797465155441400478424217075046875000000000000000000}{16807}.

$$\frac{6928538878797465155441400478424217075046875000000000000000000}{16807}$$

Factor

$$\frac{2 ^ {18} \cdot 3 ^ {81} \cdot 5 ^ {24}}{7 ^ {5}} = 4.122412613076376 \times 10^{56}\frac{6781}{16807} = 4.122412613076376 \times 10^{56}$$