Simplify the Expression: 5^2 × 5^a × 5^3 Using Exponent Rules

The product rule says $a^m \times a^n = a^{m+n}$. Think of it this way: $5^2$ means 5×5, and $5^3$ means 5×5×5. When you multiply them, you get five 5's total, which is $5^5$!

The answer stays $5^{5+a}$ no matter what! If a = 2, then you'd get $5^{5+2} = 5^7$. The algebraic form $5^{5+a}$ works for any value of a.

Great question! $(5^2)^a$ uses the power rule where you multiply exponents: $(5^2)^a = 5^{2a}$. But $5^2 \times 5^a$ uses the product rule where you add exponents.

Not unless you know the value of 'a'! $5^{5+a}$ is already in its simplest form. You could write it as $5^5 \times 5^a$ or $3125 \times 5^a$, but those are more complex.

If the bases are different (like $3^2 \times 5^a \times 7^3$), you cannot combine them using exponent rules. The product rule only works when all bases are the same!