Solve frac{5^{-2}*2^2*3^-1}{7*3^2*5^-4}

$$\frac { 5 ^ { - 2 } \times 2 ^ { 2 } \times 3 ^ { - 1 } } { 7 \times 3 ^ { 2 } \times 5 ^ { - 4 } }$$

Evaluate

$$\frac{100}{189}\approx 0.529100529$$

Solution Steps

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

$$\frac{2^{2}\times 5^{2}\times \frac{1}{3}}{7\times 3^{2}}$$

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

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

Calculate 2 to the power of 2 and get 4.

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

Calculate 5 to the power of 2 and get 25.

$$\frac{4\times 25}{7\times 3^{3}}$$

Multiply 4 and 25 to get 100.

$$\frac{100}{7\times 3^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{100}{7\times 27}$$

Multiply 7 and 27 to get 189.

$$\frac{100}{189}$$

Factor

$$\frac{2 ^ {2} \cdot 5 ^ {2}}{3 ^ {3} \cdot 7} = 0.5291005291005291$$