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You are correct. The symbol 3^{4} 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
= 2^{2} = 4, which is the 2nd power of 2,
2 × 2 × 2
= 2^{3} = 8, which is the 3rd power of 2,
2 × 2 × 2 × 2
= 2^{4} = 16, which is the 4th power of 2,

and so on.

2^{2} can also be called “2 raised to the 2nd power,” 2^{3} 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.