Solve left(2^23^-35^4right)^4/{left({2^-3{3}^2{5}^-2right)}^-3}

$$\frac{ { \left( { 2 }^{ 2 } { 3 }^{ -3 } { 5 }^{ 4 } \right) }^{ 4 } }{ { \left( { 2 }^{ -3 } { 3 }^{ 2 } { 5 }^{ -2 } \right) }^{ -3 } }$$

Evaluate

$$\frac{9765625}{1458}\approx 6697.959533608$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

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

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{\left(4\times \frac{1}{27}\times 5^{4}\right)^{4}}{\left(2^{-3}\times 3^{2}\times 5^{-2}\right)^{-3}}$$

Multiply 4 and \frac{1}{27} to get \frac{4}{27}.

$$\frac{\left(\frac{4}{27}\times 5^{4}\right)^{4}}{\left(2^{-3}\times 3^{2}\times 5^{-2}\right)^{-3}}$$

Calculate 5 to the power of 4 and get 625.

$$\frac{\left(\frac{4}{27}\times 625\right)^{4}}{\left(2^{-3}\times 3^{2}\times 5^{-2}\right)^{-3}}$$

Multiply \frac{4}{27} and 625 to get \frac{2500}{27}.

$$\frac{\left(\frac{2500}{27}\right)^{4}}{\left(2^{-3}\times 3^{2}\times 5^{-2}\right)^{-3}}$$

Calculate \frac{2500}{27} to the power of 4 and get \frac{39062500000000}{531441}.

$$\frac{\frac{39062500000000}{531441}}{\left(2^{-3}\times 3^{2}\times 5^{-2}\right)^{-3}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{\frac{39062500000000}{531441}}{\left(\frac{1}{8}\times 3^{2}\times 5^{-2}\right)^{-3}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\frac{39062500000000}{531441}}{\left(\frac{1}{8}\times 9\times 5^{-2}\right)^{-3}}$$

Multiply \frac{1}{8} and 9 to get \frac{9}{8}.

$$\frac{\frac{39062500000000}{531441}}{\left(\frac{9}{8}\times 5^{-2}\right)^{-3}}$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{\frac{39062500000000}{531441}}{\left(\frac{9}{8}\times \frac{1}{25}\right)^{-3}}$$

Multiply \frac{9}{8} and \frac{1}{25} to get \frac{9}{200}.

$$\frac{\frac{39062500000000}{531441}}{\left(\frac{9}{200}\right)^{-3}}$$

Calculate \frac{9}{200} to the power of -3 and get \frac{8000000}{729}.

$$\frac{\frac{39062500000000}{531441}}{\frac{8000000}{729}}$$

Divide \frac{39062500000000}{531441} by \frac{8000000}{729} by multiplying \frac{39062500000000}{531441} by the reciprocal of \frac{8000000}{729}.

$$\frac{39062500000000}{531441}\times \frac{729}{8000000}$$

Multiply \frac{39062500000000}{531441} and \frac{729}{8000000} to get \frac{9765625}{1458}.

$$\frac{9765625}{1458}$$

Factor

$$\frac{5 ^ {10}}{2 \cdot 3 ^ {6}} = 6697\frac{1399}{1458} = 6697.959533607682$$