Simplify 5×5^8: Solving an Exponential Multiplication Problem

Writing $5 = 5^1$ helps you see the pattern clearly! Now you can apply the rule $a^m \times a^n = a^{m+n}$ because both terms have the same base with visible exponents.

Remember: when you multiply powers with the same base, you add the exponents. When you raise a power to a power, you multiply the exponents. Don't mix these up!

You could, but $5^8 = 390,625$, so $5 \times 390,625 = 1,953,125$. It's much easier to use the exponent rule and leave your answer as $5^9$!

$5^9$ is the simplest form because it's a single power with the smallest possible exponent. You can't reduce it further using exponent rules.

If you had something like $3 \times 5^8$, you cannot combine them using exponent rules because the bases (3 and 5) are different. The multiplication rule only works with the same base!