Question

simplify.
$left(y^{3}
ight)^{-2}$
write your answer without using negative exponents.

Explanation:

Step1: Apply power of a power rule

To simplify \((y^{3})^{-2}\), we use the power of a power rule, which states that \((a^{m})^{n}=a^{m\times n}\). So, for \((y^{3})^{-2}\), we multiply the exponents: \(3\times(-2) = -6\). Thus, \((y^{3})^{-2}=y^{-6}\).

Step2: Convert negative exponent to positive

A negative exponent rule states that \(a^{-n}=\frac{1}{a^{n}}\) (where \(a
eq0\) and \(n\) is a positive integer). So, for \(y^{-6}\), we can rewrite it as \(\frac{1}{y^{6}}\) to eliminate the negative exponent.

Answer:

\(\frac{1}{y^{6}}\)