Solve 2^29/25{5^25sqrt{frac{3/5}}}

$${ 2 }^{ 2 } \frac{ 9 }{ 2 \frac { 5 } { { 5 }^{ 2 } 5 \sqrt{ \frac{ 3 }{ 5 } } } }$$

Evaluate

$$90\sqrt{15}\approx 348.568501159$$

Solution Steps

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

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

Calculate 2 to the power of 2 and get 4.

$$4\times \frac{9}{2\times \frac{5}{5^{3}\sqrt{\frac{3}{5}}}}$$

Calculate 5 to the power of 3 and get 125.

$$4\times \frac{9}{2\times \frac{5}{125\sqrt{\frac{3}{5}}}}$$

Rewrite the square root of the division \sqrt{\frac{3}{5}} as the division of square roots \frac{\sqrt{3}}{\sqrt{5}}.

$$4\times \frac{9}{2\times \frac{5}{125\times \frac{\sqrt{3}}{\sqrt{5}}}}$$

Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$4\times \frac{9}{2\times \frac{5}{125\times \frac{\sqrt{3}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}}}$$

The square of \sqrt{5} is 5.

$$4\times \frac{9}{2\times \frac{5}{125\times \frac{\sqrt{3}\sqrt{5}}{5}}}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$4\times \frac{9}{2\times \frac{5}{125\times \frac{\sqrt{15}}{5}}}$$

Cancel out 5, the greatest common factor in 125 and 5.

$$4\times \frac{9}{2\times \frac{5}{25\sqrt{15}}}$$

Rationalize the denominator of \frac{5}{25\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$4\times \frac{9}{2\times \frac{5\sqrt{15}}{25\left(\sqrt{15}\right)^{2}}}$$

The square of \sqrt{15} is 15.

$$4\times \frac{9}{2\times \frac{5\sqrt{15}}{25\times 15}}$$

Cancel out 5 in both numerator and denominator.

$$4\times \frac{9}{2\times \frac{\sqrt{15}}{5\times 15}}$$

Multiply 5 and 15 to get 75.

$$4\times \frac{9}{2\times \frac{\sqrt{15}}{75}}$$

Express 2\times \frac{\sqrt{15}}{75} as a single fraction.

$$4\times \frac{9}{\frac{2\sqrt{15}}{75}}$$

Divide 9 by \frac{2\sqrt{15}}{75} by multiplying 9 by the reciprocal of \frac{2\sqrt{15}}{75}.

$$4\times \frac{9\times 75}{2\sqrt{15}}$$

Rationalize the denominator of \frac{9\times 75}{2\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$4\times \frac{9\times 75\sqrt{15}}{2\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$4\times \frac{9\times 75\sqrt{15}}{2\times 15}$$

Multiply 9 and 75 to get 675.

$$4\times \frac{675\sqrt{15}}{2\times 15}$$

Multiply 2 and 15 to get 30.

$$4\times \frac{675\sqrt{15}}{30}$$

Divide 675\sqrt{15} by 30 to get \frac{45}{2}\sqrt{15}.

$$4\times \frac{45}{2}\sqrt{15}$$

Express 4\times \frac{45}{2} as a single fraction.

$$\frac{4\times 45}{2}\sqrt{15}$$

Multiply 4 and 45 to get 180.

$$\frac{180}{2}\sqrt{15}$$

Divide 180 by 2 to get 90.

$$90\sqrt{15}$$