Question

rewrite the expression without using a negative exponent.
\\(\dfrac{1}{2y^{-2}}\\)
simplify your answer as much as possible.

Explanation:

Step1: Recall the negative exponent rule

The rule for negative exponents is \(a^{-n}=\frac{1}{a^{n}}\), so \(\frac{1}{a^{-n}} = a^{n}\). We apply this to the term with the negative exponent in the denominator.
Given the expression \(\frac{1}{2y^{-2}}\), we can rewrite \(y^{-2}\) using the negative exponent rule.

Step2: Apply the negative exponent rule to \(y^{-2}\)

Using \(a^{-n}=\frac{1}{a^{n}}\), we know that \(\frac{1}{y^{-2}}=y^{2}\). So we can rewrite the original expression:
\(\frac{1}{2y^{-2}}=\frac{1}{2}\times\frac{1}{y^{-2}}=\frac{1}{2}\times y^{2}\)

Step3: Simplify the expression

Multiplying \(\frac{1}{2}\) and \(y^{2}\) gives \(\frac{y^{2}}{2}\).

Answer:

\(\frac{y^{2}}{2}\)