Question

What is the simplest form of (assume that a ≠ 0 and b ≠ 0)? 18ab³ / 18b⁴

A. 1/b
B. a/b
C. 1/b³
D. a/b⁴

Answer 1

The simplest form of the expression 18ab³ / 18b⁴ is a/b⁴, obtained by simplifying the fraction by its greatest common divisor.

Step-by-step explanation:

The expression can be simplified by dividing both the numerator and the denominator by the greatest common divisor (gcd), which in this case is 18b3. When we divide both the numerator and the denominator by 18b3, we simplify the expression to its simplest form:

\(\frac{18ab^3}{18b^4} = \frac{18}{18} \cdot \frac{a}{b} \cdot \frac{b^3}{b^4}\)

This simplifies further to:

\(1 \cdot \frac{a}{b} \cdot \frac{1}{b}\) since \(\frac{18}{18}=1\) and \(\frac{b^3}{b^4}=\frac{1}{b}\).

Therefore, the simplest form of the given expression is a/b4.

Calculation step included: Dividing both the numerator and the denominator by the gcd (18b3) to simplify the fraction.