Solve 144^frac{1{2}}div64^5frac{2{3}}*2561/2/frac{2{3}}

$$144 ^ { \frac { 1 } { 2 } } \div 64 ^ { 5 \frac { 2 } { 3 } } \times 256 \frac { \frac { 1 } { 2 } } { \frac { 2 } { 3 } }$$

Evaluate

$$\frac{9}{67108864}\approx 0.000000134$$

Solution Steps

Calculate 144 to the power of \frac{1}{2} and get 12.

$$\frac{12}{64^{\frac{5\times 3+2}{3}}}\times 256\times \frac{\frac{1}{2}}{\frac{2}{3}}$$

Multiply 5 and 3 to get 15.

$$\frac{12}{64^{\frac{15+2}{3}}}\times 256\times \frac{\frac{1}{2}}{\frac{2}{3}}$$

Add 15 and 2 to get 17.

$$\frac{12}{64^{\frac{17}{3}}}\times 256\times \frac{\frac{1}{2}}{\frac{2}{3}}$$

Calculate 64 to the power of \frac{17}{3} and get 17179869184.

$$\frac{12}{17179869184}\times 256\times \frac{\frac{1}{2}}{\frac{2}{3}}$$

Reduce the fraction \frac{12}{17179869184} to lowest terms by extracting and canceling out 4.

$$\frac{3}{4294967296}\times 256\times \frac{\frac{1}{2}}{\frac{2}{3}}$$

Multiply \frac{3}{4294967296} and 256 to get \frac{3}{16777216}.

$$\frac{3}{16777216}\times \frac{\frac{1}{2}}{\frac{2}{3}}$$

Divide \frac{1}{2} by \frac{2}{3} by multiplying \frac{1}{2} by the reciprocal of \frac{2}{3}.

$$\frac{3}{16777216}\times \frac{1}{2}\times \frac{3}{2}$$

Multiply \frac{1}{2} and \frac{3}{2} to get \frac{3}{4}.

$$\frac{3}{16777216}\times \frac{3}{4}$$

Multiply \frac{3}{16777216} and \frac{3}{4} to get \frac{9}{67108864}.

$$\frac{9}{67108864}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {26}} = 1.341104507446289 \times 10^{-7}$$