1. **State the problem:** Calculate the value of $10 \cdot 10^7$. 2. **Recall the rule for multiplication with powers of 10:** When multiplying powers of 10, you add the exponents if the bases are the same. 3. **Rewrite the expression:** $10 \cdot 10^7 = 10^1 \cdot 10^7$ 4. **Add the exponents:** $$10^{1+7} = 10^8$$ 5. **Evaluate the power:** $10^8 = 100000000$ 6. **Final answer:** $10 \cdot 10^7 = 100000000$