Solve frac{sqrt{4*9}*2^8}{sqrt{27*8*3^19*2^3}}

$$\frac { \sqrt { 4 \times 9 } \times 2 ^ { 8 } } { \sqrt { 27 \times 8 \times 3 ^ { 19 } \times 2 ^ { 3 } } }$$

Evaluate

$$\frac{64}{59049}\approx 0.001083846$$

Solution Steps

Multiply 4 and 9 to get 36.

$$\frac{\sqrt{36}\times 2^{8}}{\sqrt{27\times 8\times 3^{19}\times 2^{3}}}$$

Calculate the square root of 36 and get 6.

$$\frac{6\times 2^{8}}{\sqrt{27\times 8\times 3^{19}\times 2^{3}}}$$

Calculate 2 to the power of 8 and get 256.

$$\frac{6\times 256}{\sqrt{27\times 8\times 3^{19}\times 2^{3}}}$$

Multiply 6 and 256 to get 1536.

$$\frac{1536}{\sqrt{27\times 8\times 3^{19}\times 2^{3}}}$$

Multiply 27 and 8 to get 216.

$$\frac{1536}{\sqrt{216\times 3^{19}\times 2^{3}}}$$

Calculate 3 to the power of 19 and get 1162261467.

$$\frac{1536}{\sqrt{216\times 1162261467\times 2^{3}}}$$

Multiply 216 and 1162261467 to get 251048476872.

$$\frac{1536}{\sqrt{251048476872\times 2^{3}}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{1536}{\sqrt{251048476872\times 8}}$$

Multiply 251048476872 and 8 to get 2008387814976.

$$\frac{1536}{\sqrt{2008387814976}}$$

Calculate the square root of 2008387814976 and get 1417176.

$$\frac{1536}{1417176}$$

Reduce the fraction \frac{1536}{1417176} to lowest terms by extracting and canceling out 24.

$$\frac{64}{59049}$$

Factor

$$\frac{2 ^ {6}}{3 ^ {10}} = 0.0010838456197395383$$