Here are some problems that involve simplifying exponential expressions:

1. Simplify:
   $(x^3 \cdot x^4)$

2. Simplify:
   $\frac{y^7}{y^3}$

3. Simplify:
   $(2a^3b^2)^2$

4. Simplify:
   $\frac{3x^5y^2}{6x^2y}$

5. Simplify:
   $(m^4)^3 \cdot m^{-5}$

If you'd like solutions or explanations for any of these, let me know!

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Here’s a tip: Remember, when multiplying terms with the same base, add the exponents. When dividing, subtract the exponents.