Solve (4/45)^-5/(frac{4{15})^-5}

$$\frac { ( \frac { 4 } { 45 } ) ^ { - 5 } } { ( \frac { 4 } { 15 } ) ^ { - 5 } }$$

Evaluate

$$243$$

Solution Steps

Calculate \frac{4}{45} to the power of -5 and get \frac{184528125}{1024}.

$$\frac{\frac{184528125}{1024}}{\left(\frac{4}{15}\right)^{-5}}$$

Calculate \frac{4}{15} to the power of -5 and get \frac{759375}{1024}.

$$\frac{\frac{184528125}{1024}}{\frac{759375}{1024}}$$

Divide \frac{184528125}{1024} by \frac{759375}{1024} by multiplying \frac{184528125}{1024} by the reciprocal of \frac{759375}{1024}.

$$\frac{184528125}{1024}\times \frac{1024}{759375}$$

Multiply \frac{184528125}{1024} and \frac{1024}{759375} to get 243.

$$243$$

Factor

$$3^{5}$$