Given the function \( g(p) = 4^p \) and \( p = \frac{3}{2} \), we can calculate \( g(p) \) as follows:

\[
g\left(\frac{3}{2}\right) = 4^{\frac{3}{2}}
\]

This expression can be rewritten as:

\[
4^{\frac{3}{2}} = \left(4^{\frac{1}{2}}\right)^3
\]

Since \( 4^{\frac{1}{2}} = \sqrt{4} = 2 \), we have:

\[
4^{\frac{3}{2}} = 2^3 = 8
\]

Therefore, \( g\left(\frac{3}{2}\right) = 8 \).

Would you like further details or have any questions about this solution?

Here are some related questions you might find interesting:

1. What is \( g(p) \) when \( p = 2 \)?
2. How would \( g(p) \) change if the base of the exponent were 2 instead of 4?
3. Can you express \( g(p) \) in logarithmic form?
4. What is the derivative of \( g(p) \) with respect to \( p \)?
5. What is the value of \( g(p) \) for \( p = -\frac{3}{2} \)?
6. How would you solve \( g(p) = 16 \) for \( p \)?
7. What is the value of \( g(p) \) if \( p \) is an integer?
8. How does \( g(p) \) behave as \( p \) approaches infinity?

**Tip:** When dealing with exponents, breaking them down into simpler forms, like roots and powers, can make calculations easier.

Learn how to calculate g(p) = 4^p when p = 3/2. Step-by-step solution provided, breaking down the exponential function into simpler forms for easier calculation. Suitable for high school students studying exponents and powers.

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