Question
What does the exponent in an expression indicate?
Ask by Ross Spencer. in South Africa
Dec 28,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The exponent in an expression shows how many times the base is multiplied by itself. For example, in
Solution
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
Here are a few key points about exponents:
-
Positive Exponents: If
is a positive integer, (n times). -
Zero Exponent: Any non-zero number raised to the power of zero is equal to 1, i.e.,
(where ). -
Negative Exponents: A negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent, i.e.,
(where ). -
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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The exponent in an expression tells you how many times to multiply the base number by itself. For example, in
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!
