power

A power is a base raised to an exponent — the whole package, like 2^5 or x^3. People also loosely say “the power” to mean just the exponent, as in “raise it to the fourth power,” so the word does double duty.

When we say “a power of 2,” we mean a number you get by multiplying 2 by itself some whole number of times: 1, 2, 4, 8, 16, and so on (note 2^0 = 1 counts). Powers are the building blocks of exponential growth, scientific notation, and place value, so the idea shows up everywhere from compound interest to computer memory measured in powers of 2.

Be careful to separate the two uses. “Raise 5 to the third power” tells you the exponent is 3, giving the power 5^3 = 125. The number 125 is itself “a power of 5.” Context usually makes clear whether “power” means the exponent or the resulting value.