Simplification of Algebraic Exponential Expressions

In this problem, we need to simplify the expression: open parenthesis, two, a, b to the fourth power, close parenthesis squared, multiplied by, open parenthesis, a, b, close parenthesis to the fifth power.

Let's write down the expression and recall the Power of a Product rule. This rule states that when you have a product raised to a power, you apply that power to each factor inside the parentheses.

Applying this to the first part, we square the two, the a, and the b to the fourth power. For the second part, we raise both a and b to the fifth power.

Now, let's simplify individual terms. Two squared is four. For the power of a power, like b to the fourth squared, we multiply the exponents to get b to the eighth.

Next, we group the like terms together: the constants, the a terms, and the b terms.