Solve (frac{5*3^{2}*5^4}{3^255^8})^-2=

$$( \frac { 5 \cdot 3 ^ { 2 } \cdot 5 ^ { 4 } } { 3 ^ { 25 } 5 ^ { 8 } } ) ^ { - 2 } =$$

Evaluate

$$138483408119570329623890625$$

Solution Steps

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

$$\left(\frac{5^{5}\times 3^{2}}{3^{25}\times 5^{8}}\right)^{-2}$$

Cancel out 3^{2}\times 5^{5} in both numerator and denominator.

$$\left(\frac{1}{3^{23}\times 5^{3}}\right)^{-2}$$

Calculate 3 to the power of 23 and get 94143178827.

$$\left(\frac{1}{94143178827\times 5^{3}}\right)^{-2}$$

Calculate 5 to the power of 3 and get 125.

$$\left(\frac{1}{94143178827\times 125}\right)^{-2}$$

Multiply 94143178827 and 125 to get 11767897353375.

$$\left(\frac{1}{11767897353375}\right)^{-2}$$

Calculate \frac{1}{11767897353375} to the power of -2 and get 138483408119570329623890625.

$$138483408119570329623890625$$

Factor

$$3^{46}\times 5^{6}$$