Solve {left(frac{1/5right)}^-2left(5^1right)^2}{5*5^-2}

$$\frac{ { \left( \frac{ 1 }{ 5 } \right) }^{ -2 } { \left( { 5 }^{ 1 } \right) }^{ 2 } }{ 5 \times { 5 }^{ -2 } }$$

Evaluate

$$3125$$

Solution Steps

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

$$\frac{\left(\frac{1}{5}\right)^{-2}\times 5^{2}}{5\times 5^{-2}}$$

To multiply powers of the same base, add their exponents. Add 1 and -2 to get -1.

$$\frac{\left(\frac{1}{5}\right)^{-2}\times 5^{2}}{5^{-1}}$$

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

$$\left(\frac{1}{5}\right)^{-2}\times 5^{3}$$

Calculate \frac{1}{5} to the power of -2 and get 25.

$$25\times 5^{3}$$

Calculate 5 to the power of 3 and get 125.

$$25\times 125$$

Multiply 25 and 125 to get 3125.

$$3125$$

Factor

$$5^{5}$$