The problem asks to evaluate the expression $5 + 3^x$ for two different values of $x$: $x = -2$ and $x = 3$.

(a) When $x = -2$:

The expression becomes: $5 + 3^{-2}$ Recall that $3^{-2} = \frac{1}{3^2} = \frac{1}{9}$.

So, the expression simplifies to: $5 + \frac{1}{9} = \frac{45}{9} + \frac{1}{9} = \frac{46}{9}$ Thus, the answer for part (a) is: $\frac{46}{9}$

(b) When $x = 3$:

The expression becomes: $5 + 3^3$ Since $3^3 = 27$, the expression simplifies to: $5 + 27 = 32$ Thus, the answer for part (b) is: $32$

To summarize:

• (a) The expression is $\frac{46}{9}$ when $x = -2$.
• (b) The expression is $32$ when $x = 3$.

Would you like further explanations or additional questions?

Here are some related questions:

1. How do you simplify expressions involving negative exponents?
2. What is the general rule for evaluating expressions with powers of numbers?
3. How can you evaluate expressions with fractional exponents?
4. What are some real-world applications of exponential expressions?
5. How would you approach simplifying an expression with multiple terms involving exponents?

Tip: When dealing with exponents, remember that negative exponents mean you take the reciprocal of the base raised to the positive exponent.