Solve [(5^7/5^2)*5^5]^3

$$[ ( \frac { 5 ^ { 7 } } { 5 ^ { 2 } } ) \times 5 ^ { 5 } ] ^ { 3 }$$

Evaluate

$$931322574615478515625$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 7 to get 5.

$$\left(5^{5}\times 5^{5}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 5 and 5 to get 10.

$$\left(5^{10}\right)^{3}$$

Calculate 5 to the power of 10 and get 9765625.

$$9765625^{3}$$

Calculate 9765625 to the power of 3 and get 931322574615478515625.

$$931322574615478515625$$

Factor

$$5^{30}$$