Simplify a^(-5) × a^8 × x^3: Combining Multiple Exponents

Reduce the following equation:

$a^{-5}\times a^8\times x^3=$

Video Solution

Solution Steps

00:00 Simplify the following problem

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

00:07 equals the same base raised to the sum of the exponents (N+M)

00:10 We'll apply this formula to our exercise, one operation at a time

00:13 We'll maintain the base and add the exponents together

00:20 This is the solution

Step-by-Step Solution

To simplify the given mathematical expression, we'll follow these steps:

Step 1: Apply the Product of Powers Property to terms with the same base. For the expression $a^{-5} \times a^8$ , we use the rule:
$a^m \times a^n = a^{m+n}$ .
Step 2: Add the exponents: $-5 + 8 = 3$ . Therefore, $a^{-5} \times a^8 = a^3$ .
Step 3: Since $x^3$ does not share the base $a$ , it remains as is in the expression.

Therefore, the simplified form of the expression $a^{-5} \times a^8 \times x^3$ is:

$a^3 \times x^3$