Question
Do you UNDERSTAND? 5. Vocabulary A positive exponent shows repeated multiplication. What repeated operation does a negative exponent show?
Ask by Alexander Ayala. in the United States
Jan 27,2025
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Answer
A negative exponent shows repeated division.
Solution
Yes, I understand your question.
A negative exponent indicates repeated division. Specifically, a negative exponent \( -n \) can be expressed as:
\[
a^{-n} = \frac{1}{a^n}
\]
This means that instead of multiplying the base \( a \) by itself \( n \) times, you are dividing 1 by \( a \) multiplied by itself \( n \) times.
For example:
- \( 2^{-3} = \frac{1}{2^3} = \frac{1}{8} \)
So, the repeated operation that a negative exponent shows is division.
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Simplify this solution The Deep Dive
A negative exponent indicates that you’re dealing with the reciprocal of the base raised to the corresponding positive exponent. So, for example, \( a^{-n} \) means \( \frac{1}{a^n} \). It’s like flipping the fraction upside down! If you had \( 2^{-3} \), it would be interpreted as \( \frac{1}{2^3} \), which equals \( \frac{1}{8} \). This concept of negative exponents pops up all over the place, especially in scientific notation! When you have really big or tiny numbers, it makes things a lot easier to express them succinctly. Instead of writing 0.0001 as a decimal, you can use \( 1 \times 10^{-4} \). Perfect for impressing your friends with your math skills!
