Solve 5^4*5^-7/(5^2)^-2

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

Evaluate

$$5$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and -7 to get -3.

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

To raise a power to another power, multiply the exponents. Multiply 2 and -2 to get -4.

$$\frac{5^{-3}}{5^{-4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -4 from -3 to get 1.

$$5^{1}$$

Calculate 5 to the power of 1 and get 5.

$$5$$

Factor

$$5$$