Solve (frac{10^{3}*5^{2}*7}{4^2*5^4*5^2})^2

$$( \frac { 10 ^ { 3 } \cdot 5 ^ { 2 } \cdot 7 } { 4 ^ { 2 } \cdot 5 ^ { 4 } \cdot 5 ^ { 2 } } ) ^ { 2 }$$

Evaluate

$$\frac{49}{100}=0.49$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\left(\frac{10^{3}\times 5^{2}\times 7}{4^{2}\times 5^{6}}\right)^{2}$$

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

$$\left(\frac{7\times 10^{3}}{4^{2}\times 5^{4}}\right)^{2}$$

Calculate 10 to the power of 3 and get 1000.

$$\left(\frac{7\times 1000}{4^{2}\times 5^{4}}\right)^{2}$$

Multiply 7 and 1000 to get 7000.

$$\left(\frac{7000}{4^{2}\times 5^{4}}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$\left(\frac{7000}{16\times 5^{4}}\right)^{2}$$

Calculate 5 to the power of 4 and get 625.

$$\left(\frac{7000}{16\times 625}\right)^{2}$$

Multiply 16 and 625 to get 10000.

$$\left(\frac{7000}{10000}\right)^{2}$$

Reduce the fraction \frac{7000}{10000} to lowest terms by extracting and canceling out 1000.

$$\left(\frac{7}{10}\right)^{2}$$

Calculate \frac{7}{10} to the power of 2 and get \frac{49}{100}.

$$\frac{49}{100}$$

Factor

$$\frac{7 ^ {2}}{2 ^ {2} \cdot 5 ^ {2}} = 0.49$$