Solve 5^2/6^6div2/5^2

$$\frac{ { 5 }^{ 2 } }{ { 6 }^{ 6 } } \div \frac{ 2 }{ { 5 }^{ 2 } }$$

Evaluate

$$\frac{625}{93312}\approx 0.00669796$$

Solution Steps

Divide \frac{5^{2}}{6^{6}} by \frac{2}{5^{2}} by multiplying \frac{5^{2}}{6^{6}} by the reciprocal of \frac{2}{5^{2}}.

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

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

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

Calculate 5 to the power of 4 and get 625.

$$\frac{625}{6^{6}\times 2}$$

Calculate 6 to the power of 6 and get 46656.

$$\frac{625}{46656\times 2}$$

Multiply 46656 and 2 to get 93312.

$$\frac{625}{93312}$$

Factor

$$\frac{5 ^ {4}}{2 ^ {7} \cdot 3 ^ {6}} = 0.006697959533607681$$