Solve 5⁴ × 25: Multiplying Powers of 5

Think of factoring! Ask yourself: what number times itself equals 25? Since $5 \times 5 = 25$, we can write $25 = 5^2$.

You could calculate $5^4 = 625$ and then $625 \times 25 = 15,625$, but converting to common bases is faster and helps you recognize the pattern $5^6$!

Look for prime factorization! Break each number into its prime factors. If they share common prime factors, you can often find a common base to work with.

Multiplication: $a^m \times a^n = a^{m+n}$ (add exponents)
Power of power: $(a^m)^n = a^{m \times n}$ (multiply exponents)

Use smaller examples to verify the rule works: $5^2 \times 5^1 = 25 \times 5 = 125$ and $5^{2+1} = 5^3 = 125$ ✓