91Ó°ÊÓ

Simplify the expression, and rationalize the denominator when appropriate. $$\sqrt[3]{\frac{3 x^{2} y^{5}}{4 x}}$$

Express as a sum of terms of the form , where r is a rational number. $$\frac{\left(x^{2}+2\right)^{2}}{x^{5}}$$

Simplify the expression, and rationalize the denominator when appropriate. $$\sqrt[4]{\frac{5 x^{8} y^{3}}{27 x^{2}}}$$

Express as a sum of terms of the form , where r is a rational number. $$\frac{(\sqrt{x}-3)^{2}}{x^{3}}$$

Simplify the expression, and rationalize the denominator when appropriate. $$\sqrt[4]{\frac{x^{7} y^{12}}{125 x}}$$

Below the cloud base, the air temperature \(T\left(\text { in }^{\circ} \mathrm{F}\right)\) at height \(h\) (in feet) can be approximated by the equation \(T=T_{0}-\left(\frac{5.5}{1000}\right) h,\) where \(T_{0}\) is the temperature at ground level. (a) Determine the air temperature at a height of 1 mile if the ground temperature is \(70^{\circ} \mathrm{F}\). (b) At what altitude is the temperature freezing?

Express as a quotient. $$x^{-3}+x^{2}$$

Simplify the expression, and rationalize the denominator when appropriate. $$\sqrt[5]{\frac{5 x^{7} y^{2}}{8 x^{3}}}$$

The height \(h\) (in feet) of the cloud base can be estimated using \(h=227(T-D),\) where \(T\) is the ground temperature and \(D\) is the dew point. (a) If the temperature is \(70^{\circ} \mathrm{F}\) and the dew point is \(55^{\circ} \mathrm{F}\), find the height of the cloud base. (b) If the dew point is \(65^{\circ} \mathrm{F}\) and the cloud base is 3500 feet, estimate the ground temperature.

Simplify the expression, and rationalize the denominator when appropriate. $$\sqrt[5]{\frac{3 x^{11} y^{3}}{9 x^{2}}}$$