Simplify a^(-3x) × a^b × a^b: Exponent Multiplication Practice

The multiplication rule for exponents states that $a^m \times a^n = a^{m+n}$. Think of it this way: $a^2 \times a^3 = (a \cdot a) \times (a \cdot a \cdot a) = a^5$, which is 2 + 3 = 5, not 2 × 3 = 6!

Since $a^b \times a^b$ means you have the same exponent twice, you add: $b + b = 2b$. It's like adding any like terms in algebra!

No, this is the simplified form! Since $-3x$ and $2b$ are different variable terms, they cannot be combined further. The expression is fully simplified.

The process is identical! For example: $a^{-6} \times a^4 \times a^4 = a^{-6+4+4} = a^2$. Just add all the exponents together, whether they're numbers or variables.

Treat negative exponents just like negative numbers in addition. For $-3x + b + b$, you get $-3x + 2b$. The negative sign stays with the 3x term.