Simplify the Expression: 6^t × 9^t Using Laws of Exponents

The rule $a^m \times a^n = a^{m+n}$ only works when the bases are identical. Since 6 and 9 are different bases, you must use the product rule: $a^m \times b^m = (a \times b)^m$.

Same base, different exponents: Add the exponents
Different bases, same exponents: Combine the bases
Example: $2^3 \times 2^4 = 2^7$ but $2^3 \times 5^3 = (2 \times 5)^3$

$(6 \times 9)^t$ means 54 raised to the power t, while $(6 \times 9)^{2t}$ means 54 raised to the power 2t. The first is correct because we're multiplying two terms each with exponent t, not adding exponents.

Yes! Since $6 \times 9 = 54$, you can write the final answer as $54^t$. Both forms are mathematically equivalent and correct.

Absolutely! $a^m \times b^m \times c^m = (a \times b \times c)^m$. For example: $2^3 \times 3^3 \times 4^3 = (2 \times 3 \times 4)^3 = 24^3$.