You are correct. The symbol 34 means “the product formed by using 3 as a factor four times.”
You can form an entire series of products by using a particular number as a factor twice, three times, four times, etc. These products are called the powers of the number. Thus:
2 × 2
= 22 = 4, which is the 2nd power of 2,
2 × 2 × 2
= 23 = 8, which is the 3rd power of 2,
2 × 2 × 2 × 2
= 24 = 16, which is the 4th power of 2,
and so on.
22 can also be called “2 raised to the 2nd power,” 23 can also be called “2 raised to the 3rd power,” an so on.
The 2nd power of 3, that is, 3 raised to the 2nd power, would be the number formed by using 3 as a factor twice.
