Question

simplify the expression.\\(\frac{4a^{8}b^{9}}{8ab^{5}}\\)

Explanation:

Step1: Simplify the coefficients

$\frac{4}{8} = \frac{1}{2}$

Step2: Simplify the $a$-terms

Use exponent rule $\frac{a^m}{a^n}=a^{m-n}$:
$a^{8-1}=a^7$

Step3: Simplify the $b$-terms

Use exponent rule $\frac{b^m}{b^n}=b^{m-n}$:
$b^{9-5}=b^4$

Step4: Combine all simplified parts

Multiply the results from Steps 1-3.

Answer:

$\frac{1}{2}a^7b^4$