Simplify the Expression: 6^-5 × 6^2 Using Laws of Exponents

Insert the corresponding expression:

$$$6^{-5}\times6^2=$

Let's solve the problem step-by-step:

• Step 1: Identify the base and exponents involved.
• Step 2: Apply the exponent multiplication rule to simplify.
• Step 3: Further simplify the expression if necessary.

Now, we will work through each step:

Step 1: The problem gives us the expression $6^{-5} \times 6^2$. We have a common base, which is 6.

Step 2: Using the rule for multiplying exponents with the same base, we add the exponents. Thus, $6^{-5} \times 6^2 = 6^{-5+2} = 6^{-3}$.

Step 3: Simplifying further, since a negative exponent means the reciprocal, we have:
$6^{-3} = \frac{1}{6^3}$.

Therefore, the solution to the problem is: $\frac{1}{6^3}$.