Question

1. $\frac{2b^{4}}{2a^{3}b^{3}}$

Explanation:

Step1: Cancel common numerical factors

The numerator and denominator both have a factor of 2, so divide both by 2:
$\frac{2b^4}{2a^3b^3} = \frac{b^4}{a^3b^3}$

Step2: Simplify variable $b$ using exponent rules

Use the quotient rule for exponents: $b^m \div b^n = b^{m-n}$. Here, $m=4$, $n=3$:
$\frac{b^4}{a^3b^3} = \frac{b^{4-3}}{a^3} = \frac{b^1}{a^3}$

Step3: Write simplified form

$b^1$ can be written as $b$:
$\frac{b}{a^3}$

Answer:

$\frac{b}{a^3}$