Solve (5^{2}*5^3*5^4):(5^6-5^2)

$$( 5 ^ { 2 } \cdot 5 ^ { 3 } \cdot 5 ^ { 4 } ) : ( 5 ^ { 6 } - 5 ^ { 2 } )$$

Evaluate

$$\frac{78125}{624}\approx 125.200320513$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{5^{5}\times 5^{4}}{5^{6}-5^{2}}$$

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

$$\frac{5^{9}}{5^{6}-5^{2}}$$

Calculate 5 to the power of 9 and get 1953125.

$$\frac{1953125}{5^{6}-5^{2}}$$

Calculate 5 to the power of 6 and get 15625.

$$\frac{1953125}{15625-5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{1953125}{15625-25}$$

Subtract 25 from 15625 to get 15600.

$$\frac{1953125}{15600}$$

Reduce the fraction \frac{1953125}{15600} to lowest terms by extracting and canceling out 25.

$$\frac{78125}{624}$$

Factor

$$\frac{5 ^ {7}}{2 ^ {4} \cdot 3 \cdot 13} = 125\frac{125}{624} = 125.20032051282051$$