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

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

Evaluate

$$312500$$

Solution Steps

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

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

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

$$\frac{5^{9}\times 2^{4}}{2^{2}\times 5^{2}}$$

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

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

Calculate 2 to the power of 2 and get 4.

$$4\times 5^{7}$$

Calculate 5 to the power of 7 and get 78125.

$$4\times 78125$$

Multiply 4 and 78125 to get 312500.

$$312500$$

Factor

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