To solve the expression $\left(\frac{3}{8}\right)^5 \times \left(\frac{3}{8}\right)^8$, you need to use the properties of exponents. Specifically, when multiplying two powers with the same base, you add the exponents.

The expression can be rewritten as:

$\left(\frac{3}{8}\right)^5 \times \left(\frac{3}{8}\right)^8 = \left(\frac{3}{8}\right)^{5+8} = \left(\frac{3}{8}\right)^{13}$

So the simplified expression is:

$\left(\frac{3}{8}\right)^{13}$

Would you like any further details or have any questions?

Here are 5 related questions you might find interesting:

1. What happens when you multiply two fractions together?
2. How do you simplify an expression with different exponents?
3. Can you express $\left(\frac{3}{8}\right)^{13}$ as a decimal?
4. What is the general rule for multiplying powers with the same base?
5. How do you simplify an expression like $\left(\frac{3}{8}\right)^a \times \left(\frac{3}{8}\right)^b$ in terms of $a$ and $b$?

Tip: When dealing with powers, always remember that multiplying similar bases results in adding the exponents.