Powers with a natural exponent
To write a product of equal factors briefly we use a power: the product of n factors equal to a is written aⁿ. Here a is the base, n is the exponent, and the value of aⁿ is the result of the product: 3⁴ = 3 · 3 · 3 · 3 = 81. a² is read “a squared”, a³ “a cubed”; the first power of a number equals the number itself: a¹ = a. For a negative base the sign depends on the exponent: an even exponent gives a positive result and an odd exponent a negative one; (-2)⁴ = 16, (-2)³ = -8, but -2⁴ = -16 because the power is done first. Raising to a power is a third-stage operation. Writing a number greater than 10 as a · 10ⁿ with 1 ≤ a < 10 and n a natural number is called the standard form of the number.
“Power cards”: pupils draw two cards (a base and an exponent), read the power, write it as a product and compute it. They predict the sign for even or odd exponents beforehand.