Question

simplify. express your answer using positive exponents. \\(\frac{h^{8}}{h^{9}}\\)

Explanation:

Step1: Apply exponent quotient rule

When dividing exponents with the same base, subtract the exponents: $\frac{h^a}{h^b}=h^{a - b}$. Here, $a = 8$ and $b = 9$, so $\frac{h^8}{h^9}=h^{8 - 9}$.

Step2: Simplify the exponent

Calculate $8 - 9=-1$, so we have $h^{-1}$.

Step3: Convert to positive exponent

Using the rule $a^{-n}=\frac{1}{a^n}$, $h^{-1}=\frac{1}{h^1}=\frac{1}{h}$.

Answer:

$\frac{1}{h}$