Question

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

Explanation:

Step1: Apply power of a power rule

When raising a power to a power, we multiply the exponents. The formula for \((a^m)^n\) is \(a^{m\times n}\). For \((y^2)^{-2}\), we multiply the exponents 2 and -2.
\((y^2)^{-2}=y^{2\times(-2)}\)

Step2: Calculate the exponent

Calculate \(2\times(-2)\) which equals -4. So we have \(y^{-4}\).

Step3: Convert negative exponent to positive

A negative exponent \(a^{-n}\) is equal to \(\frac{1}{a^n}\). So \(y^{-4}=\frac{1}{y^4}\)

Answer:

\(\frac{1}{y^4}\)