Pregunta

What does the exponent in an expression indicate?

Ask by Ross Spencer. in South Africa
Dec 28,2024

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The exponent in an expression shows how many times the base is multiplied by itself. For example, in , the base is multiplied by itself times.

Solución

The exponent in an expression indicates how many times the base is multiplied by itself. It is a shorthand notation used in mathematics to represent repeated multiplication.
For example, in the expression :
  • is the base.
  • is the exponent.
This means that is multiplied by itself times.
Here are a few key points about exponents:
  1. Positive Exponents: If is a positive integer, (n times).
  2. Zero Exponent: Any non-zero number raised to the power of zero is equal to 1, i.e., (where ).
  3. Negative Exponents: A negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent, i.e., (where ).
  4. Fractional Exponents: A fractional exponent indicates a root. For example, represents the -th root of .
Understanding exponents is fundamental in algebra and is used in various mathematical concepts, including polynomial expressions, scientific notation, and exponential growth or decay models.

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Mind Expander

The exponent in an expression tells you how many times to multiply the base number by itself. For example, in , the exponent 4 means you multiply 3 by itself four times: , which equals 81. It’s a shorthand way of expressing repeated multiplication, making calculations easier and more manageable!
Exponents also hold the key to understanding exponential growth, which appears in various real-world scenarios, like populations, investments, and technology advancements. For instance, if a population doubles every year, you can express this growth with exponents, illustrating how quickly things can scale up. So, watch out—those numbers can grow faster than you might think!

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