The value of $7^{2.2}$ approximates to 72.313 when rounded to three decimal places.

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Here are 5 related questions for practice:

1. What is $8^{2.5}$ rounded to three decimal places?
2. Approximate $6^{1.7}$ to three decimal places.
3. What is $9^{2.3}$ rounded to three decimal places?
4. Calculate $5^{3.2}$ and round it to three decimal places.
5. Approximate $4^{2.1}$ to three decimal places.

Tip: When dealing with non-integer exponents, try breaking the base and exponent into simpler components for mental approximation!