Question 1

Simplify the following expression:





The following pictures are the exponent laws. You can use them as reference.

Select and check your answer...

A. 3²
B. 3^-2
C. 9²
D. 9^-2

Notice that the base for both terms are not the same. So, we need to find a way to make the them the same.

Now, to make these bases the same, note that:

                     9 = 3 x 3
                        = 3²

Replacing 9 with 3², we have:

                  (3²)² x 3^-2

To proceed, we need to simplify the term:

                    (3²)²

Using the exponent law as shown in the picture, we get:


               (3²)² = 3^{2 x 2}

                                   

Now, 2 multiply by 2  gives 4.    

To proceed, we need to simplify:

                    3⁴ x 3^-2

Using the exponent law as shown in the picture, we get:


               3⁴ x 3^-2 = 3^{4 +(- 2)}
                          = 3^{4 - 2}
                                   

Now, 4 minus 2 gives 2.

Finally, we have the simplest term: 3²

Therefore, the answer is A.