Question

6^{-5} cdot 6^{3} cdot 6 =

Explanation:

Step1: Apply exponent product rule

When multiplying terms with the same base, add exponents: $a^m \cdot a^n = a^{m+n}$. Here, $6 = 6^1$, so:
$6^{-5} \cdot 6^3 \cdot 6^1 = 6^{-5+3+1}$

Step2: Calculate exponent sum

Compute the sum of the exponents:
$-5 + 3 + 1 = -1$

Step3: Rewrite negative exponent

A negative exponent means the reciprocal: $a^{-k} = \frac{1}{a^k}$
$6^{-1} = \frac{1}{6}$

Answer:

$\frac{1}{6}$