Solve ((5/3)^3)^4/(frac{5{2})^14}=

$$\frac { ( ( \frac { 5 } { 3 } ) ^ { 3 } ) ^ { 4 } } { ( \frac { 5 } { 2 } ) ^ { 14 } } =$$

Evaluate

$$\frac{16384}{13286025}\approx 0.001233175$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{\left(\frac{5}{3}\right)^{12}}{\left(\frac{5}{2}\right)^{14}}$$

Calculate \frac{5}{3} to the power of 12 and get \frac{244140625}{531441}.

$$\frac{\frac{244140625}{531441}}{\left(\frac{5}{2}\right)^{14}}$$

Calculate \frac{5}{2} to the power of 14 and get \frac{6103515625}{16384}.

$$\frac{\frac{244140625}{531441}}{\frac{6103515625}{16384}}$$

Divide \frac{244140625}{531441} by \frac{6103515625}{16384} by multiplying \frac{244140625}{531441} by the reciprocal of \frac{6103515625}{16384}.

$$\frac{244140625}{531441}\times \frac{16384}{6103515625}$$

Multiply \frac{244140625}{531441} and \frac{16384}{6103515625} to get \frac{16384}{13286025}.

$$\frac{16384}{13286025}$$

Factor

$$\frac{2 ^ {14}}{3 ^ {12} \cdot 5 ^ {2}} = 0.0012331754606814303$$