Expand the Expression: Solving 2^(2a+a) Step by Step

Expand the following equation:

$2^{2a+a}=$

Video Solution

Solution Steps

00:06 Let's find out which expressions match the original one.

00:10 Remember, when multiplying exponents with the same base, like A,

00:14 we raise A to the power of N plus M.

00:18 We'll now apply this rule to our exercise.

00:22 Keep the base and add the exponents together.

00:26 We can see that this expression isn't the same as the original.

00:32 Let's use the same method to simplify the other expressions.

00:39 Now this one matches the original expression.

00:43 Since this uses addition, not multiplication, it doesn't fit.

00:47 And that's how we find the solution!

Step-by-Step Solution

To solve the problem, we can follow these steps:

Step 1: Recognize that the given expression is $2^{2a+a}$ .
Step 2: Use the Power of a Power Rule for exponents, which allows us to write $a^{m+n} = a^m \times a^n$ .
Step 3: Rewrite the expression as follows:

Given: $2^{2a+a}$

Step 4: Simplify the exponent by splitting it:

Since the expression in the exponent is $2a+a$ , we can write:

$2^{2a+a} = 2^{2a} \times 2^a$

Thus, applying the properties of exponents correctly leads us to the expanded form.

Therefore, the expanded equation is $2^{2a} \times 2^a$ .