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

Insert the corresponding expression:

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

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 According to the exponent laws, the multiplication of exponents with equal bases (A)

00:09 equals the same base raised to the sum of the exponents (N+M)

00:13 We'll apply this formula to our exercise

00:19 We'll maintain the base and add the exponents together

00:33 According to the exponent laws, any number with a negative exponent (-N)

00:36 equals its reciprocal raised to the opposite exponent (N)

00:39 We'll apply this formula to our exercise

00:42 We'll convert to the reciprocal and raise to the opposite exponent

00:48 This is the solution

Step-by-Step Solution

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

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: $\frac{1}{6^3}$ .