Solve =-49/4(1/sqrt{(32)^3})

$$= - \frac { 49 } { 4 } ( \frac { 1 } { \sqrt { ( 32 ) ^ { 3 } } } )$$

Evaluate

$$-\frac{49\sqrt{2}}{1024}\approx -0.067672329$$

Solution Steps

Calculate 32 to the power of 3 and get 32768.

$$-\frac{49}{4}\times \frac{1}{\sqrt{32768}}$$

Factor 32768=128^{2}\times 2. Rewrite the square root of the product \sqrt{128^{2}\times 2} as the product of square roots \sqrt{128^{2}}\sqrt{2}. Take the square root of 128^{2}.

$$-\frac{49}{4}\times \frac{1}{128\sqrt{2}}$$

Rationalize the denominator of \frac{1}{128\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$-\frac{49}{4}\times \frac{\sqrt{2}}{128\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$-\frac{49}{4}\times \frac{\sqrt{2}}{128\times 2}$$

Multiply 128 and 2 to get 256.

$$-\frac{49}{4}\times \frac{\sqrt{2}}{256}$$

Multiply -\frac{49}{4} times \frac{\sqrt{2}}{256} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-49\sqrt{2}}{4\times 256}$$

Multiply 4 and 256 to get 1024.

$$\frac{-49\sqrt{2}}{1024}$$