Solving for a in an Exponential Equation

Hi Selin, let's solve this exponential equation together step by step.

First, let's write down the equation given in the problem: two to the power of three a, times three to the power of three a, times six to the power of two a, equals two hundred sixteen to the power of five.

Notice that the first two terms have the same exponent, three a. We can multiply their bases together using the property that x to the power of n times y to the power of n equals x times y, all to the power of n.

So, two to the power of three a times three to the power of three a becomes six to the power of three a.

Now we have the same base, six, on the left. Using the rule for multiplying powers with the same base, we add the exponents together: three a plus two a gives us five a.