Question

q2 simplify the expression.
\\(\frac{-24ab^3}{14a^2b^2}\\)
\\(\bigcirc\frac{-2b}{a}\\)
\\(\bigcirc\frac{-12ab}{7}\\)
\\(\bigcirc\frac{-12b}{7a}\\)
\\(\bigcirc\frac{-12b^5}{7a^3}\\)

Explanation:

Step1: Simplify coefficients

Find the greatest common divisor (GCD) of -24 and 14. The GCD of 24 and 14 is 2. Divide both -24 and 14 by 2:
$\frac{-24\div2}{14\div2} = \frac{-12}{7}$

Step2: Simplify variable \(a\)

Using the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$, for \(a\) terms: $\frac{a}{a^2}=a^{1-2}=a^{-1}=\frac{1}{a}$

Step3: Simplify variable \(b\)

Using the rule of exponents for \(b\) terms: $\frac{b^3}{b^2}=b^{3 - 2}=b^{1}=b$

Step4: Combine all simplified parts

Multiply the simplified coefficient, \(a\) part, and \(b\) part together:
$\frac{-12}{7}\times\frac{1}{a}\times b=\frac{-12b}{7a}$

Answer:

$\frac{-12b}{7a}$ (corresponding to the option: $\boldsymbol{\frac{-12b}{7a}}$)