Solve frac{2^{2}*3^{-5}*5^{3}*7^-3}{2^-4*3^3*5^2}

$$\frac { 2 ^ { 2 } \cdot 3 ^ { - 5 } \cdot 5 ^ { 3 } \cdot 7 ^ { - 3 } } { 2 ^ { - 4 } \cdot 3 ^ { 3 } \cdot 5 ^ { 2 } }$$

Evaluate

$$\frac{320}{2250423}\approx 0.000142195$$

Solution Steps

Cancel out 5^{2} in both numerator and denominator.

$$\frac{5\times 2^{2}\times 3^{-5}\times 7^{-3}}{2^{-4}\times 3^{3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{5\times 2^{6}\times 3^{-5}\times 7^{-3}}{3^{3}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{5\times 2^{6}\times 7^{-3}}{3^{8}}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{5\times 64\times 7^{-3}}{3^{8}}$$

Multiply 5 and 64 to get 320.

$$\frac{320\times 7^{-3}}{3^{8}}$$

Calculate 7 to the power of -3 and get \frac{1}{343}.

$$\frac{320\times \frac{1}{343}}{3^{8}}$$

Multiply 320 and \frac{1}{343} to get \frac{320}{343}.

$$\frac{\frac{320}{343}}{3^{8}}$$

Calculate 3 to the power of 8 and get 6561.

$$\frac{\frac{320}{343}}{6561}$$

Express \frac{\frac{320}{343}}{6561} as a single fraction.

$$\frac{320}{343\times 6561}$$

Multiply 343 and 6561 to get 2250423.

$$\frac{320}{2250423}$$

Factor

$$\frac{2 ^ {6} \cdot 5}{3 ^ {8} \cdot 7 ^ {3}} = 0.00014219548947020183$$