To simplify the expression [tex]\( y^{-9} \)[/tex], let's go through a step-by-step explanation:
1. Understanding the Negative Exponent:
- The expression [tex]\( y^{-9} \)[/tex] contains a negative exponent, [tex]\(-9\)[/tex].
- A negative exponent means that we take the reciprocal of the base [tex]\( y \)[/tex]. Specifically, [tex]\( a^{-b} = \frac{1}{a^b} \)[/tex].
2. Applying the Rule:
- Using the rule for negative exponents, we can rewrite [tex]\( y^{-9} \)[/tex] as:
[tex]\[
y^{-9} = \frac{1}{y^9}
\][/tex]
3. Simplified Expression:
- The expression [tex]\( \frac{1}{y^9} \)[/tex] is the simplified form of [tex]\( y^{-9} \)[/tex].
Therefore, the step-by-step simplification of [tex]\( y^{-9} \)[/tex] is:
[tex]\[
y^{-9} = \frac{1}{y^9}
\][/tex]
This is the final simplified form of the given expression.
