Expand the Power Expression: Calculate 9^12 Step by Step

Great observation! While 6 + 2 = 8, we need the exponents to add up to 12, not 8. The question asks for $9^{12}$, so we need combinations like 8 + 4 = 12.

Look for pairs that add up to the original exponent. For $9^{12}$, valid pairs include: 1+11, 2+10, 3+9, 4+8, 5+7, 6+6. Check which option matches!

When multiplying powers with the same base: $a^m \times a^n = a^{m+n}$. Keep the base the same and add the exponents together.

Absolutely! You could write $9^{12} = 9^3 \times 9^4 \times 9^5$ since 3+4+5=12. The key is that all exponents must add to 12.

Because $9^8 \times 9^4 = 9^{8+4} = 9^{12}$ by the product rule. The exponents 8 and 4 add up to exactly 12, matching our original expression!