Simplify the Expression: 9×9⁹ Power and Multiplication Problem

Video Solution

Solution Steps

00:06 Let's simplify this expression together.

00:09 Here's a helpful rule to remember: when we multiply terms with the same base A, we keep the base and add the exponents.

00:17 So, A to the power of N times A to the power of M becomes A to the power of N plus M.

00:23 Remember another useful rule: any number raised to the power of 1 is just the number itself.

00:29 Now, let's apply these rules to our problem.

00:33 We'll add the exponents together and keep our base, giving us our simplified answer.

00:39 And there we have it! That's our simplified solution.

Step-by-Step Solution

To solve this problem, let's apply the multiplication of powers rule:

Now, we'll work through the calculation step-by-step:

Step 1: Rewrite $9$ as $9^1$ . Thus, our expression becomes $9^1 \times 9^9$ .

Step 2: Use the exponent rule to combine: $9^1 \times 9^9 = 9^{1+9}$ .

Step 3: Simplify the exponent by adding: $9^{1+9} = 9^{10}$ .

Therefore, the simplified form of the expression is $9^{10}$ .

In terms of the answer choices, the correct answer is

$9^{1+9}$