Solve (5^{-3})^{-2}*(2^{4}*5^7)div(2^2*5^2)^5

$$( 5 ^ { - 3 } ) ^ { - 2 } \cdot ( 2 ^ { 4 } \cdot 5 ^ { 7 } ) \div ( 2 ^ { 2 } \cdot 5 ^ { 2 } ) ^ { 5 }$$

Evaluate

$$\frac{125}{64}=1.953125$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 6 and 7 to get 13.

$$\frac{5^{13}\times 2^{4}}{\left(2^{2}\times 5^{2}\right)^{5}}$$

Calculate 5 to the power of 13 and get 1220703125.

$$\frac{1220703125\times 2^{4}}{\left(2^{2}\times 5^{2}\right)^{5}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{1220703125\times 16}{\left(2^{2}\times 5^{2}\right)^{5}}$$

Multiply 1220703125 and 16 to get 19531250000.

$$\frac{19531250000}{\left(2^{2}\times 5^{2}\right)^{5}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{19531250000}{\left(4\times 5^{2}\right)^{5}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{19531250000}{\left(4\times 25\right)^{5}}$$

Multiply 4 and 25 to get 100.

$$\frac{19531250000}{100^{5}}$$

Calculate 100 to the power of 5 and get 10000000000.

$$\frac{19531250000}{10000000000}$$

Reduce the fraction \frac{19531250000}{10000000000} to lowest terms by extracting and canceling out 156250000.

$$\frac{125}{64}$$

Factor

$$\frac{5 ^ {3}}{2 ^ {6}} = 1\frac{61}{64} = 1.953125$$