What is $$b^{\frac{\scriptstyle4y}{\scriptstyle9x}} \times b^{-\frac{\scriptstyle3y}{\scriptstyle10x}}$$?

$$b^\frac{\scriptstyle13y}{\scriptstyle90x}$$

$$b^\frac{\scriptstyle3}{\scriptstyle7x}$$

$$b^\frac{\scriptstyle16y}{\scriptstyle45x}$$

$$b^\frac{\scriptstyle6y}{\scriptstyle23x}$$

$$b^{-\frac{\scriptstyle9x}{\scriptstyle5x}}$$

What is $$c^\frac{\scriptstyle7}{\scriptstyle3} \times c^{-\frac{\scriptstyle4}{\scriptstyle2}} \times c^\frac{\scriptstyle2x}{\scriptstyle3}$$?

$$c^{\frac{\scriptstyle2x + 1}{\scriptstyle3}}$$

$$c^{\frac{\scriptstyle3x + 2}{\scriptstyle2}}$$

$$c^\frac{\scriptstyle2x}{\scriptstyle3} + a^\frac{\scriptstyle1}{\scriptstyle3}$$

a^{\frac{2}{3}} \cdot a^{\frac{1}{2}}

b^{\frac{3}{5}} \cdot b^{\frac{4}{15}}

c^{- \frac{4}{12}} \cdot c^{\frac{5}{6}}

d^{\frac{1}{3}} \cdot d^{- \frac{2}{7}}

e^{\frac{x}{y}} \cdot e^{\frac{4 x}{9 y}}

k^{\frac{1}{3}} \cdot k^{\frac{4}{10}}