Solve (frac{5}15^2)^3*(35/25)^2

$$( \frac { 5 } { 15 } ^ { 2 } ) ^ { 3 } \cdot ( \frac { 35 } { 25 } ) ^ { 2 }$$

Evaluate

$$\frac{49}{18225}\approx 0.002688615$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\left(\frac{5}{15}\right)^{6}\times \left(\frac{35}{25}\right)^{2}$$

Reduce the fraction \frac{5}{15} to lowest terms by extracting and canceling out 5.

$$\left(\frac{1}{3}\right)^{6}\times \left(\frac{35}{25}\right)^{2}$$

Calculate \frac{1}{3} to the power of 6 and get \frac{1}{729}.

$$\frac{1}{729}\times \left(\frac{35}{25}\right)^{2}$$

Reduce the fraction \frac{35}{25} to lowest terms by extracting and canceling out 5.

$$\frac{1}{729}\times \left(\frac{7}{5}\right)^{2}$$

Calculate \frac{7}{5} to the power of 2 and get \frac{49}{25}.

$$\frac{1}{729}\times \frac{49}{25}$$

Multiply \frac{1}{729} and \frac{49}{25} to get \frac{49}{18225}.

$$\frac{49}{18225}$$

Factor

$$\frac{7 ^ {2}}{3 ^ {6} \cdot 5 ^ {2}} = 0.0026886145404663923$$