Exponents

In an algebra class, Mr. Thompson shows his students a sheet of paper and asks what will happen if he keeps folding it in half.

He folds the paper once and counts two layers. After a second fold, the paper has two times two or four layers. After a third fold, the paper has two times two times two, or eight layers.

Each fold doubles the number of layers, creating a pattern of repeated multiplication.

Repeated multiplication can be represented using exponent notation, a to the power of n. Here, a is the base, the number that is multiplied repeatedly, and n is the exponent, which shows how many times the base is multiplied.

In the paper-folding example, the expression two times two times two can be written as two to the power of three. Since the number two appears three times, the base is two and the exponent is three.

Exponents represent very large numbers efficiently. For example, the distance from Earth to Proxima Centauri is approximately four times ten to the power of thirteen kilometers. Ten to the power of thirteen means multiplying thirteen factors of ten, showing repeated multiplication.