Solve frac{2^{-3}*3^5}{2^-7-3^6}*5^6

$$\frac { 2 ^ { - 3 } \cdot 3 ^ { 5 } } { 2 ^ { - 7 } - 3 ^ { 6 } } \cdot 5 ^ { 6 }$$

Evaluate

$$-\frac{60750000}{93311}\approx -651.048643783$$

Solution Steps

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

$$\frac{\frac{1}{8}\times 3^{5}}{2^{-7}-3^{6}}\times 5^{6}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{\frac{1}{8}\times 243}{2^{-7}-3^{6}}\times 5^{6}$$

Multiply \frac{1}{8} and 243 to get \frac{243}{8}.

$$\frac{\frac{243}{8}}{2^{-7}-3^{6}}\times 5^{6}$$

Calculate 2 to the power of -7 and get \frac{1}{128}.

$$\frac{\frac{243}{8}}{\frac{1}{128}-3^{6}}\times 5^{6}$$

Calculate 3 to the power of 6 and get 729.

$$\frac{\frac{243}{8}}{\frac{1}{128}-729}\times 5^{6}$$

Subtract 729 from \frac{1}{128} to get -\frac{93311}{128}.

$$\frac{\frac{243}{8}}{-\frac{93311}{128}}\times 5^{6}$$

Divide \frac{243}{8} by -\frac{93311}{128} by multiplying \frac{243}{8} by the reciprocal of -\frac{93311}{128}.

$$\frac{243}{8}\left(-\frac{128}{93311}\right)\times 5^{6}$$

Multiply \frac{243}{8} and -\frac{128}{93311} to get -\frac{3888}{93311}.

$$-\frac{3888}{93311}\times 5^{6}$$

Calculate 5 to the power of 6 and get 15625.

$$-\frac{3888}{93311}\times 15625$$

Multiply -\frac{3888}{93311} and 15625 to get -\frac{60750000}{93311}.

$$-\frac{60750000}{93311}$$

Factor

$$-\frac{60750000}{93311} = -651\frac{4539}{93311} = -651.0486437826194$$