Simplify the Expression: 10^(a+b) × 10^(a+1) × 10^(b+1)

Reduce the following equation:

$10^{a+b}\times10^{a+1}\times10^{b+1}=$

Video Solution

Solution Steps

00:00 Simplify the following problem

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

00:06 equals the same base raised to the sum of the exponents (N+M)

00:10 We'll apply this formula to our exercise

00:14 We'll maintain the base and add the exponents together

00:31 Let's group the factors together

00:48 This is the solution

Step-by-Step Solution

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

Now, let's work through each step:

Step 1: The original expression is $10^{a+b} \times 10^{a+1} \times 10^{b+1}$ .

Step 2: Since the base (10) is the same for all terms, we add the exponents:

(a+b) + (a+1) + (b+1)

Step 3: Simplifying further:

a + b + a + 1 + b + 1 = 2a + 2b + 2

Thus, the expression simplifies to:

10^{2a + 2b + 2}

Therefore, the solution to the problem is $10^{2b+2a+2}$ .