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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?).

Find the value of \(3^{-3}\).

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What is the value of \( (-4)^{-2} \)?

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What is the value of the following expression:

\[ 5^{-1} \times 2^3 \times 3^{-2} ? \]

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Scientific notation has two parts: a number (say \(a\)) between one and ten, and that number multiplied by ten raised to the power \(b,\) where \(b\) is a non-zero integer: e.g. \( a \times 10^{b}, \) where \(1 \le a<10 \).

Find the value of \(a\) when you simplify the following expression in scientific notation to two decimal points:

\[(4.7 \times 10^{-3}) \times (6.1 \times 10^{9}). \]

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Find the value of \( \left( \frac{1}{4} \right)^{-2} \).

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