Simplify the Expression: 6^t × 9^t Using Laws of Exponents

Question

Insert the corresponding expression:

$6^t\times9^t=$

00:00 Simplify the following problem

00:03 According to the laws of exponents, a product raised to a power (N)

00:08 Equals the product where each factor is raised to the same power (N)

00:13 We will apply this formula to our exercise

00:20 This is the solution

To solve this problem, we'll follow these steps:

Step 1: Identify the expression to simplify, [ $6^t \times 9^t$ ].
Step 2: Apply the Power of a Product Rule, [ $a^m \times b^m = (a \times b)^m$ ].

Now, let's work through each step:

Step 1: We start with the expression $6^t \times 9^t$ .

Step 2: Using the Power of a Product Rule, we rewrite this expression as $(6 \times 9)^t$ .

Thus, the correct equivalent expression is $\left(6 \times 9\right)^t$ .

$\left(6\times9\right)^t$