Solve (5^{-1})^{-2}*(2^{4}*5^7)div(2^2*5^2)^5

$$( 5 ^ { - 1 } ) ^ { - 2 } \cdot ( 2 ^ { 4 } \cdot 5 ^ { 7 } ) \div ( 2 ^ { 2 } \cdot 5 ^ { 2 } ) ^ { 5 }$$

Evaluate

$$\frac{1}{320}=0.003125$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -1 and -2 to get 2.

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

To multiply powers of the same base, add their exponents. Add 2 and 7 to get 9.

$$\frac{5^{9}\times 2^{4}}{\left(2^{2}\times 5^{2}\right)^{5}}$$

Calculate 5 to the power of 9 and get 1953125.

$$\frac{1953125\times 2^{4}}{\left(2^{2}\times 5^{2}\right)^{5}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{1953125\times 16}{\left(2^{2}\times 5^{2}\right)^{5}}$$

Multiply 1953125 and 16 to get 31250000.

$$\frac{31250000}{\left(2^{2}\times 5^{2}\right)^{5}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{31250000}{\left(4\times 5^{2}\right)^{5}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{31250000}{\left(4\times 25\right)^{5}}$$

Multiply 4 and 25 to get 100.

$$\frac{31250000}{100^{5}}$$

Calculate 100 to the power of 5 and get 10000000000.

$$\frac{31250000}{10000000000}$$

Reduce the fraction \frac{31250000}{10000000000} to lowest terms by extracting and canceling out 31250000.

$$\frac{1}{320}$$

Factor

$$\frac{1}{2 ^ {6} \cdot 5} = 0.003125$$