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

Reduce the following equation:

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

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

• Step 1: Identify the exponents in the given expression.
• Step 2: Use the property of exponents for multiplication by like bases.
• Step 3: Add the exponents together and simplify.

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:

Step 3: Simplifying further:

Thus, the expression simplifies to:

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