Expand t^9: Writing Out the Ninth Power Expression

While $t^9 \times t^1$ technically equals $t^{10}$, not $t^9$! When you multiply powers with the same base, you add the exponents: 9 + 1 = 10. The goal is to break down $t^9$ into smaller powers that add up to 9.

Absolutely! You could write $t^5 \times t^4$, $t^1 \times t^1 \times t^7$, or even $t^1 \times t^1 \times t^1 \times t^1 \times t^1 \times t^1 \times t^1 \times t^1 \times t^1$. As long as the exponents add up to 9, it's correct!

To expand means to write the expression as a product of simpler terms. Instead of having one big exponent, you're breaking it down into smaller pieces that multiply together to give the same result.

Always double-check by adding up all the small exponents! In $t^4 \times t^2 \times t^3$, check that 4 + 2 + 3 = 9. If the sum doesn't equal your original exponent, you made an error.

For this problem, stick with positive exponents since we're expanding $t^9$ (a positive power). Negative exponents would make the math more complicated and aren't needed here.