Solve 5^4:[5^4:(5^2*5)]^2

$$5 ^ { 4 } : [ 5 ^ { 4 } : ( 5 ^ { 2 } \cdot 5 ) ] ^ { 2 }$$

Evaluate

$$25$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{5^{4}}{\left(\frac{5^{4}}{5^{3}}\right)^{2}}$$

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

$$\frac{5^{4}}{\left(5^{1}\right)^{2}}$$

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

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 4 to get 2.

$$5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25$$

Factor

$$5^{2}$$