Question

exponents and exponential functions
rewriting an algebraic expression without a negative exponent
rewrite the expression without using a negative exponent.
-4n⁻⁵
simplify your answer as much as possible.

Explanation:

Step1: Recall negative exponent rule

The rule for negative exponents is \( a^{-n}=\frac{1}{a^{n}} \) (where \( a
eq0 \) and \( n \) is a positive integer). In the expression \( -4n^{-5} \), the base with the negative exponent is \( n \), not -4 (since the exponent applies only to the base it is attached to, here \( n \)).

Step2: Apply the negative exponent rule

Using the rule \( a^{-n}=\frac{1}{a^{n}} \), we can rewrite \( n^{-5} \) as \( \frac{1}{n^{5}} \). So the expression \( -4n^{-5} \) becomes \( -4\times\frac{1}{n^{5}} \).

Step3: Simplify the expression

Multiplying -4 and \( \frac{1}{n^{5}} \), we get \( \frac{-4}{n^{5}} \) or \( -\frac{4}{n^{5}} \).

Answer:

\( -\dfrac{4}{n^{5}} \)