Solve (3/5)^-2:(3/5)^5=

$$( \frac { 3 } { 5 } ) ^ { - 2 } : ( \frac { 3 } { 5 } ) ^ { 5 } =$$

Evaluate

$$\frac{78125}{2187}\approx 35.722450846$$

Solution Steps

Rewrite \left(\frac{3}{5}\right)^{5} as \left(\frac{3}{5}\right)^{-2}\times \left(\frac{3}{5}\right)^{7}. Cancel out \left(\frac{3}{5}\right)^{-2} in both numerator and denominator.

$$\frac{1}{\left(\frac{3}{5}\right)^{7}}$$

Calculate \frac{3}{5} to the power of 7 and get \frac{2187}{78125}.

$$\frac{1}{\frac{2187}{78125}}$$

Divide 1 by \frac{2187}{78125} by multiplying 1 by the reciprocal of \frac{2187}{78125}.

$$1\times \frac{78125}{2187}$$

Multiply 1 and \frac{78125}{2187} to get \frac{78125}{2187}.

$$\frac{78125}{2187}$$

Factor

$$\frac{5 ^ {7}}{3 ^ {7}} = 35\frac{1580}{2187} = 35.72245084590764$$