Solve sqrt{frac{3^{10}*5^{7}*8^{3}*1^{20}*25}{2^{6}*5^2*3^8*5^7*2^3}}

$$\sqrt { \frac { 3 ^ { 10 } \cdot 5 ^ { 7 } \cdot 8 ^ { 3 } \cdot 1 ^ { 20 } \cdot 25 } { 2 ^ { 6 } \cdot 5 ^ { 2 } \cdot 3 ^ { 8 } \cdot 5 ^ { 7 } \cdot 2 ^ { 3 } } }$$

Evaluate

$$3$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$\sqrt{\frac{3^{10}\times 5^{7}\times 8^{3}\times 1^{20}\times 25}{2^{9}\times 5^{2}\times 3^{8}\times 5^{7}}}$$

To multiply powers of the same base, add their exponents. Add 2 and 7 to get 9.

$$\sqrt{\frac{3^{10}\times 5^{7}\times 8^{3}\times 1^{20}\times 25}{2^{9}\times 5^{9}\times 3^{8}}}$$

Cancel out 3^{8}\times 5^{7} in both numerator and denominator.

$$\sqrt{\frac{25\times 1^{20}\times 3^{2}\times 8^{3}}{2^{9}\times 5^{2}}}$$

Calculate 1 to the power of 20 and get 1.

$$\sqrt{\frac{25\times 1\times 3^{2}\times 8^{3}}{2^{9}\times 5^{2}}}$$

Multiply 25 and 1 to get 25.

$$\sqrt{\frac{25\times 3^{2}\times 8^{3}}{2^{9}\times 5^{2}}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{\frac{25\times 9\times 8^{3}}{2^{9}\times 5^{2}}}$$

Multiply 25 and 9 to get 225.

$$\sqrt{\frac{225\times 8^{3}}{2^{9}\times 5^{2}}}$$

Calculate 8 to the power of 3 and get 512.

$$\sqrt{\frac{225\times 512}{2^{9}\times 5^{2}}}$$

Multiply 225 and 512 to get 115200.

$$\sqrt{\frac{115200}{2^{9}\times 5^{2}}}$$

Calculate 2 to the power of 9 and get 512.

$$\sqrt{\frac{115200}{512\times 5^{2}}}$$

Calculate 5 to the power of 2 and get 25.

$$\sqrt{\frac{115200}{512\times 25}}$$

Multiply 512 and 25 to get 12800.

$$\sqrt{\frac{115200}{12800}}$$

Divide 115200 by 12800 to get 9.

$$\sqrt{9}$$

Calculate the square root of 9 and get 3.

$$3$$

Factor

$$3$$