Simplify Powers of 10: 10^5 × 10^7 × 10^2 Step by Step

The product rule says $a^m \times a^n = a^{m+n}$. Think of it this way: $10^5$ means five 10s multiplied together, so when you multiply by $10^7$, you're adding 7 more 10s to the chain!

The product rule only works with the same base! For example, $2^3 \times 5^4$ cannot be simplified using this rule. All terms must have the same base number.

Think "same base, add the power"! When you see the same number being raised to different powers and multiplied together, just add those powers up.

$10^{14}$ equals 100,000,000,000,000 (that's 100 trillion!). Each power of 10 represents the number of zeros after the 1.

You could write out all the multiplication: $(10×10×10×10×10) × (10×10×10×10×10×10×10) × (10×10)$, but that's 14 tens multiplied together - much harder than just adding 5+7+2!