Question

write the expression as a single power.
$(-6)^5\cdot (-6)^4=\quad (-6)^9$
how can you write any expression of the form $a^m\cdot a^n$ as a single power?
$a^m\cdot a^n=?$
options: $a^{m + n}$, $a^{m - n}$, $a^{mn}$, $a^{m\div n}$

Explanation:

Step1: Apply exponent product rule

For $(-6)^5 \cdot (-6)^4$, use $a^m \cdot a^n = a^{m+n}$.
$\boldsymbol{(-6)^{5+4}=(-6)^9}$

Step2: Identify general exponent rule

The product of same-base powers adds exponents.
$\boldsymbol{a^m \cdot a^n = a^{m+n}}$

Answer:

1. $(-6)^9$
2. $a^{m+n}$