1. **Problem statement:** Calculate the value of the expression $4^2 + 2^3 + 7^2$. 2. **Recall the rules:** - $a^b$ means $a$ multiplied by itself $b$ times. - Calculate each power separately, then add the results. 3. **Calculate each term:** - $4^2 = 4 \times 4 = 16$ - $2^3 = 2 \times 2 \times 2 = 8$ - $7^2 = 7 \times 7 = 49$ 4. **Add the results:** $$4^2 + 2^3 + 7^2 = 16 + 8 + 49$$ 5. **Sum:** $$16 + 8 = 24$$ $$24 + 49 = 73$$ 6. **Final answer:** $$\boxed{73}$$