Question

exponents and exponential functions
rewriting an algebraic expression without a negative exponent
rewrite the expression without using a negative exponent.
\\(\frac{1}{-2z^{-2}}\\)
simplify your answer as much as possible.

Explanation:

Step1: Recall the negative exponent rule

The rule for negative exponents is \( a^{-n}=\frac{1}{a^{n}} \) (where \( a
eq0 \) and \( n \) is a positive integer). So we can rewrite \( z^{-2} \) as \( \frac{1}{z^{2}} \).

Step2: Substitute the negative exponent

Substitute \( z^{-2}=\frac{1}{z^{2}} \) into the denominator \( -2z^{-2} \), we get \( -2\times\frac{1}{z^{2}}=\frac{-2}{z^{2}} \).

Step3: Simplify the fraction

Now our original expression \( \frac{1}{-2z^{-2}} \) becomes \( \frac{1}{\frac{-2}{z^{2}}} \). Dividing by a fraction is the same as multiplying by its reciprocal, so \( \frac{1}{\frac{-2}{z^{2}}}=1\times\frac{z^{2}}{-2}=-\frac{z^{2}}{2} \).

Answer:

\( -\frac{z^{2}}{2} \)