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

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

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

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

...

Simplify as much as possible and write as roots:

Simplify and write as a single power if possible:

You can find the solutions here.

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