1. **State the problem:** Calculate the value of $5^{16}$. 2. **Formula used:** The expression $a^n$ means multiplying the base $a$ by itself $n$ times. 3. **Explanation:** Here, the base is 5 and the exponent is 16, so we multiply 5 by itself 16 times. 4. **Intermediate work:** Instead of multiplying 5 sixteen times directly, we can use properties of exponents to simplify: $$5^{16} = (5^8)^2$$ Calculate $5^8$ first: $$5^8 = 5^4 \times 5^4$$ Calculate $5^4$: $$5^4 = 5 \times 5 \times 5 \times 5 = 625$$ So, $$5^8 = 625 \times 625 = 390625$$ Now square $5^8$: $$5^{16} = (390625)^2 = 152587890625$$ 5. **Final answer:** $$5^{16} = 152587890625$$