Question 1

What is a power of an integer?

Accepted Answer

A power of an integer is the result of multiplying an integer by itself a fixed number of times. The integer being multiplied is called the base, and the number of times it is multiplied is called the exponent. For example, 2 to the 5th power means 2 multiplied by itself 5 times, which equals 32. Powers are written as base^exponent, and they grow very fast as the exponent increases.

Question 2

How do you read the notation base^exponent?

Accepted Answer

Read base^exponent as the base raised to the exponent. For instance, 3^4 is read as three to the fourth power and equals 3 times 3 times 3 times 3, which is 81. Special names: an exponent of 2 is called squaring (3^2 is three squared) and an exponent of 3 is called cubing (3^3 is three cubed). Any nonzero integer raised to the 0 power equals 1 by convention.

Question 3

What range of powers does this table cover?

Accepted Answer

The table covers all 100 powers from 1 to the first power up to 10 to the tenth power. Values range from 1 (which is 1 to any power) up to 10 billion (10 to the tenth power). Each of the 10 bases from 1 through 10 has its own stack showing all 10 of its first powers in order. The full range of values spans ten orders of magnitude.

Question 4

How can I tell if a number is a power of an integer?

Accepted Answer

Type the number into the search bar and click Search. If it appears in the table as some base^exponent, the table scrolls to its stack and highlights the matching cell in yellow. If it does not appear, a not-found message confirms that the number is not equal to any of the 100 powers in the table. Note that very small numbers may appear in multiple stacks: 1 is 1 to any power, and 64 is both 2^6, 4^3, and 8^2.

Question 5

What are some common powers worth memorizing?

Accepted Answer

Powers of 2 dominate in computing: 2^10 equals 1024 (one kibibyte), 2^16 is 65536, and 2^20 is roughly one million. Powers of 10 are the basis of scientific notation: 10^3 is one thousand, 10^6 is one million, and 10^9 is one billion. Squares from 1 to 12 (1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144) and cubes from 1 to 10 (1, 8, 27, 64, 125, 216, 343, 512, 729, 1000) are standard knowledge for arithmetic and algebra.

Table of Powers base 1-10

Additional Resources

1 - 1

2 - 1024

3 - 59049

4 - 1048576

5 - 9765625

6 - 60466176

7 - 282475249

8 - 1073741824

9 - 3486784401

10 - 10000000000