Simplify 3^(-2) × 3^4: Combining Negative and Positive Exponents

The multiplication symbol is between two powers with the same base. The rule says: $a^m \times a^n = a^{m+n}$. We're adding the exponents, not the bases!

A negative exponent like $3^{-2}$ means $\frac{1}{3^2} = \frac{1}{9}$. Just treat it like any other number when adding: (-2) + 4 = 2.

You can calculate $3^2 = 9$, but the question asks to reduce the equation. In this context, $3^2$ is the simplified exponential form.

• Multiplying same bases: Add exponents → $x^a \times x^b = x^{a+b}$
• Power of a power: Multiply exponents → $(x^a)^b = x^{a \times b}$

If you had different bases like $2^3 \times 3^4$, you cannot combine them using exponent rules. The bases must be identical to use $a^m \times a^n = a^{m+n}$.