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# Exponential Functions

From compound interest to bubonic plague, things that grow or spread really fast are often modeled by exponential functions. Learn about these powerful functions (pun intended?).

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

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Which of the following is equal to \( \large \frac{ x^{-2} } { x ^ { -6}} \)?

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by **Brilliant Staff**

Simplify

\[ \left( 2 x^2 y^2 \right)^3 x^{-4} y^3. \]

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Simplify

\[ \frac{4x^{-5}y^{-3}\cdot 3x^3 y^{-2}}{ 6x^{-5} y^3}. \]

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If \( a + a^{-1} = 3 \), evaluate

\[ a^4 + a^{-4}. \]

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Which of the following is equal to \(\Large \frac{x^4}{x^{-8}}\)?

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