Let's evaluate the given exponential functions one by one:

1. $f(x) = 2^x$, find $f(-3)$:

$f(-3) = 2^{-3} = \frac{1}{2^3} = \frac{1}{8}$ So, $f(-3) = \frac{1}{8}$.

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2. $f(x) = \left(\frac{1}{3}\right)^x$, find $f(-2)$:

$f(-2) = \left(\frac{1}{3}\right)^{-2} = \left(\frac{3}{1}\right)^2 = 3^2 = 9$ So, $f(-2) = 9$.

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3. $f(x) = 4^x$, find $f(-2)$:

$f(-2) = 4^{-2} = \frac{1}{4^2} = \frac{1}{16}$ So, $f(-2) = \frac{1}{16}$.

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4. $f(x) = 5^x$, find $f(-1)$:

$f(-1) = 5^{-1} = \frac{1}{5}$ So, $f(-1) = \frac{1}{5}$.

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5. $f(x) = \left(\frac{2}{3}\right)^x$, find $f(2)$:

$f(2) = \left(\frac{2}{3}\right)^2 = \frac{2^2}{3^2} = \frac{4}{9}$ So, $f(2) = \frac{4}{9}$.

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6. $f(x) = \left(\frac{4}{3}\right)^x$, find $f(2)$:

$f(2) = \left(\frac{4}{3}\right)^2 = \frac{4^2}{3^2} = \frac{16}{9}$ So, $f(2) = \frac{16}{9}$.

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7. $f(x) = 6^x$, find $f(-1)$:

$f(-1) = 6^{-1} = \frac{1}{6}$ So, $f(-1) = \frac{1}{6}$.

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8. $f(x) = 5^{-x}$, find $f(3)$:

$f(3) = 5^{-3} = \frac{1}{5^3} = \frac{1}{125}$ So, $f(3) = \frac{1}{125}$.

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9. $f(x) = \left(\frac{1}{7}\right)^x$, find $f(1)$:

$f(1) = \left(\frac{1}{7}\right)^1 = \frac{1}{7}$ So, $f(1) = \frac{1}{7}$.

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10. $f(x) = \left(\frac{3}{4}\right)^x$, find $f(-3)$:

$f(-3) = \left(\frac{3}{4}\right)^{-3} = \left(\frac{4}{3}\right)^3 = \frac{4^3}{3^3} = \frac{64}{27}$ So, $f(-3) = \frac{64}{27}$.

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Summary of Results:

1. $f(-3) = \frac{1}{8}$
2. $f(-2) = 9$
3. $f(-2) = \frac{1}{16}$
4. $f(-1) = \frac{1}{5}$
5. $f(2) = \frac{4}{9}$
6. $f(2) = \frac{16}{9}$
7. $f(-1) = \frac{1}{6}$
8. $f(3) = \frac{1}{125}$
9. $f(1) = \frac{1}{7}$
10. $f(-3) = \frac{64}{27}$

Would you like more details or have any further questions?

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Here are 5 related questions to explore:

1. What is the general formula for evaluating $f(x) = a^x$ for negative values of $x$?
2. How does changing the base of an exponential function affect the graph of the function?
3. What happens when the base of an exponential function is between 0 and 1?
4. Can an exponential function ever equal zero? Why or why not?
5. What is the inverse of an exponential function?

Tip: When dealing with negative exponents, remember that $a^{-x} = \frac{1}{a^x}$.