Simplify 8^(-10) × 8^5 × 8^4: Exponent Reduction Problem

The rule $a^m \times a^n = a^{m+n}$ comes from how exponents work! When you multiply $8^2 \times 8^3$, you're really doing (8×8) × (8×8×8), which gives you 8 multiplied by itself 5 times total.

Negative exponents work just like regular numbers! So -10 + 5 + 4 = -1. The negative sign stays with the number when you add: think of it as owing 10, then gaining 5, then gaining 4 more.

Absolutely! You can combine $8^{-10} \times 8^5 = 8^{-5}$ first, then $8^{-5} \times 8^4 = 8^{-1}$. Addition is associative, so the order doesn't matter as long as you add all the exponents.

$8^{-1}$ means "1 divided by 8" or $\frac{1}{8}$. Negative exponents create fractions: the base goes in the denominator and the exponent becomes positive.

Count carefully: start at -10, then add 5 (now at -5), then add 4 (now at -1). You can also write it as: $(-10) + (+5) + (+4) = -10 + 9 = -1$.