Multiplying Exponents

Multiplying Exponents

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Exponents, sometimes called “powers,” are a simple way of showing repeated multiplication. As an example, multiply five by itself four times, as in 5 ✕ 5 ✕ 5 ✕ 5. Another way to express this would be as “five raised to the fourth power,” or 5⁴. In this example, the five is called the base and the four is called the exponent. The exponent is the number of times the base is multiplied by itself. To find the value of an exponent, simply perform the multiplication: 5 ✕ 5 = 25; 25 ✕ 5 = 125, and 125 ✕ 5 = 625. Therefore, 5⁴ = 625.

You must learn the rules for basic operations involving exponents. The rules for multiplication with exponents are summarized below:

• To multiply two terms with the same base and different exponents, keep the base the same and add the exponents: x^yx^z = x^y + z
  Example: 2²(2³) = 2^{2 + 3} = 2⁵ = 32
• To simplify an exponential term that has one base and two exponents, multiply the exponents: (x^y)^z = x^yz
  Example: (2²)³ = 2^{2 × 3} = 2⁶ = 64