Solve frac{2^{3}*5^{4}*2^{-1}*5^{2}}{5^3*2^-2*5^3*2^4}

$$\frac { 2 ^ { 3 } \cdot 5 ^ { 4 } \cdot 2 ^ { - 1 } \cdot 5 ^ { 2 } } { 5 ^ { 3 } \cdot 2 ^ { - 2 } \cdot 5 ^ { 3 } \cdot 2 ^ { 4 } }$$

Evaluate

$$1$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and -1 to get 2.

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

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{2^{2}\times 5^{6}}{5^{3}\times 2^{-2}\times 5^{3}\times 2^{4}}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

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

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

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

Divide 2^{2}\times 5^{6} by 5^{6}\times 2^{2} to get 1.

$$1$$

Factor

$$1$$