12:12 PM Exponents: Basic Rules | ||||
Exponents: Basic Rules (page 1 of 5) Exponents are shorthand for repeated multiplication of the same thing by itself. For instance, the shorthand for multiplying three copies of the number 5 is shown on the right-hand side of the equals sign in (5)(5)(5) = 5 3. The exponent , being 3 in this example, stands for however many times the value is being multiplied. The thing that's being multiplied, being 5 in this example, is called the base . This process of using exponents is called raising to a power , where the exponent is the power . The expression 5 3 is pronounced as five, raised to the third power or five to the third . There are two specially-named powers: to the second power is generally pronounced as squared , and to the third power is generally pronounced as cubed . So 5 3 is commonly pronounced as five cubed . When we deal with numbers, we usually just simplify; we'd rather deal with 27 than with 3 3 . But with variables, we need the exponents, because we'd rather deal with x 6 than with xxxxxx . Exponents have a few rules that we can use for simplifying expressions.
To simplify this, I can think in terms of what those exponents mean. To the third means multiplying three copies and to the fourth means multiplying four copies . Using this fact, I can expand the two factors, and then work backwards to the simplified form: (x 3 )(x 4 ) = (xxx )(xxxx ) = xxxxxxx Note that x 7 also equals x (3+4). This demonstrates the first basic exponent rule: Whenever you multiply two terms with the same base, you can add the exponents:
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