Simplify 5^(-2) × 5^(-1) × 5: Negative Exponent Reduction

The power rule states that $a^m \times a^n = a^{m+n}$. Think of it as: $5^2 \times 5^3 = (5 \times 5) \times (5 \times 5 \times 5) = 5^5$. You're combining groups of the same base!

A negative exponent means reciprocal: $5^{-2} = \frac{1}{5^2} = \frac{1}{25}$. It's the opposite of positive powers - instead of multiplying, you're dividing.

Treat them like regular addition with integers: -2 + (-1) + 1. The negative signs stay with their numbers, so you get -2 - 1 + 1 = -2.

Absolutely! Convert each term: $5^{-2} = \frac{1}{25}$, $5^{-1} = \frac{1}{5}$, and $5^1 = 5$. Then multiply: $\frac{1}{25} \times \frac{1}{5} \times 5 = \frac{1}{25}$ = $5^{-2}$ ✓

Remember: Same operation, add exponents (multiplying powers). Different operation, multiply exponents (power of a power). Since we're multiplying $5^{-2} \times 5^{-1} \times 5^1$, we add!