Question

simplify.
\frac{y^{-9}}{y^{9}}
write your answer with positive exponents only.

Explanation:

Step1: Apply exponent subtraction rule

When dividing exponents with the same base, subtract the denominator exponent from the numerator exponent: $\frac{y^a}{y^b}=y^{a-b}$
$\frac{y^{-9}}{y^{9}} = y^{-9 - 9}$

Step2: Calculate exponent value

Compute the subtraction in the exponent.
$y^{-9 - 9}=y^{-18}$

Step3: Rewrite with positive exponent

Use the rule $y^{-n}=\frac{1}{y^n}$ to convert to positive exponent.
$y^{-18}=\frac{1}{y^{18}}$

Answer:

$\frac{1}{y^{18}}$