Solve [(5^4*5*5^2)^2:7]:5+2*3^2-4

$$[ ( 5 ^ { 4 } \cdot 5 \cdot 5 ^ { 2 } ) ^ { 2 } : 7 ] : 5 + 2 \cdot 3 ^ { 2 } - 4$$

Evaluate

$$\frac{1220703223}{7}\approx 174386174.714285714$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{\frac{\left(5^{5}\times 5^{2}\right)^{2}}{7}}{5}+2\times 3^{2}-4$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{\frac{\left(5^{7}\right)^{2}}{7}}{5}+2\times 3^{2}-4$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{\frac{5^{14}}{7}}{5}+2\times 3^{2}-4$$

Express \frac{\frac{5^{14}}{7}}{5} as a single fraction.

$$\frac{5^{14}}{7\times 5}+2\times 3^{2}-4$$

Cancel out 5 in both numerator and denominator.

$$\frac{5^{13}}{7}+2\times 3^{2}-4$$

Calculate 5 to the power of 13 and get 1220703125.

$$\frac{1220703125}{7}+2\times 3^{2}-4$$

Calculate 3 to the power of 2 and get 9.

$$\frac{1220703125}{7}+2\times 9-4$$

Multiply 2 and 9 to get 18.

$$\frac{1220703125}{7}+18-4$$

Add \frac{1220703125}{7} and 18 to get \frac{1220703251}{7}.

$$\frac{1220703251}{7}-4$$

Subtract 4 from \frac{1220703251}{7} to get \frac{1220703223}{7}.

$$\frac{1220703223}{7}$$

Factor

$$\frac{37 \cdot 47 \cdot 701957}{7} = 174386174\frac{5}{7} = 174386174.7142857$$