Simplify the Product: 3^x × 7^x × 5^x Using Exponent Rules

You only add exponents when you have the same base being multiplied, like $2^3 \times 2^5 = 2^8$. Here we have different bases (3, 7, 5) with the same exponent, so we combine the bases instead!

Great question! In $3^a \times 3^b \times 3^c$, you have the same base (3) with different exponents, so you'd add exponents: $3^{a+b+c}$. In our problem, we have different bases with the same exponent.

Not necessarily! The answer $(3 \times 7 \times 5)^x$ is perfectly correct. You can simplify it to $105^x$ if needed, but both forms are mathematically equivalent.

Then you cannot combine them using exponent rules! The expression would stay as $3^x \times 7^y \times 5^z$. This rule only works when all exponents are identical.

It's the reverse of distributing! When you distribute, $(ab)^n = a^n b^n$. Here we're doing the opposite: $a^n b^n = (ab)^n$. We're factoring out the common exponent.