Solve 3^-310^-5125/5^-76^-5

$$\frac{ { 3 }^{ -3 } { 10 }^{ -5 } 125 }{ { 5 }^{ -7 } { 6 }^{ -5 } }$$

Evaluate

$$28125$$

Solution Steps

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

$$\frac{\frac{1}{27}\times 10^{-5}\times 125}{5^{-7}\times 6^{-5}}$$

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$\frac{\frac{1}{27}\times \frac{1}{100000}\times 125}{5^{-7}\times 6^{-5}}$$

Multiply \frac{1}{27} and \frac{1}{100000} to get \frac{1}{2700000}.

$$\frac{\frac{1}{2700000}\times 125}{5^{-7}\times 6^{-5}}$$

Multiply \frac{1}{2700000} and 125 to get \frac{1}{21600}.

$$\frac{\frac{1}{21600}}{5^{-7}\times 6^{-5}}$$

Calculate 5 to the power of -7 and get \frac{1}{78125}.

$$\frac{\frac{1}{21600}}{\frac{1}{78125}\times 6^{-5}}$$

Calculate 6 to the power of -5 and get \frac{1}{7776}.

$$\frac{\frac{1}{21600}}{\frac{1}{78125}\times \frac{1}{7776}}$$

Multiply \frac{1}{78125} and \frac{1}{7776} to get \frac{1}{607500000}.

$$\frac{\frac{1}{21600}}{\frac{1}{607500000}}$$

Divide \frac{1}{21600} by \frac{1}{607500000} by multiplying \frac{1}{21600} by the reciprocal of \frac{1}{607500000}.

$$\frac{1}{21600}\times 607500000$$

Multiply \frac{1}{21600} and 607500000 to get 28125.

$$28125$$

Factor

$$3^{2}\times 5^{5}$$