Solve (frac{2^{2}*5^{-5}*5^{3}}{2^-4-3^3*5^2})^-3

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

Evaluate

$$-\frac{19677533006234375}{262144}=-75063831353.12795639$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -5 and 3 to get -2.

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

Calculate 2 to the power of 2 and get 4.

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

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

$$\left(\frac{4\times \frac{1}{25}}{2^{-4}-3^{3}\times 5^{2}}\right)^{-3}$$

Multiply 4 and \frac{1}{25} to get \frac{4}{25}.

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

Calculate 2 to the power of -4 and get \frac{1}{16}.

$$\left(\frac{\frac{4}{25}}{\frac{1}{16}-3^{3}\times 5^{2}}\right)^{-3}$$

Calculate 3 to the power of 3 and get 27.

$$\left(\frac{\frac{4}{25}}{\frac{1}{16}-27\times 5^{2}}\right)^{-3}$$

Calculate 5 to the power of 2 and get 25.

$$\left(\frac{\frac{4}{25}}{\frac{1}{16}-27\times 25}\right)^{-3}$$

Multiply 27 and 25 to get 675.

$$\left(\frac{\frac{4}{25}}{\frac{1}{16}-675}\right)^{-3}$$

Subtract 675 from \frac{1}{16} to get -\frac{10799}{16}.

$$\left(\frac{\frac{4}{25}}{-\frac{10799}{16}}\right)^{-3}$$

Divide \frac{4}{25} by -\frac{10799}{16} by multiplying \frac{4}{25} by the reciprocal of -\frac{10799}{16}.

$$\left(\frac{4}{25}\left(-\frac{16}{10799}\right)\right)^{-3}$$

Multiply \frac{4}{25} and -\frac{16}{10799} to get -\frac{64}{269975}.

$$\left(-\frac{64}{269975}\right)^{-3}$$

Calculate -\frac{64}{269975} to the power of -3 and get -\frac{19677533006234375}{262144}.

$$-\frac{19677533006234375}{262144}$$

Factor

$$-\frac{19677533006234375}{262144} = -75063831353\frac{33544}{262144} = -75063831353.12796$$