Questions: Simplify to lowest terms, if possible: 27 b^2 x^3 / 63 x^2 b^2

Solution Steps

To simplify the given fraction to its lowest terms, we need to:

1. Identify and cancel out common factors in the numerator and the denominator.
2. Simplify the remaining expression.

Given the fraction: \[ \frac{27 b^{2} x^{3}}{63 x^{2} b^{2}} \] we first identify the common factors in the numerator and the denominator. Both the numerator and the denominator have the factors \(b^2\) and \(x^2\).

Cancel out the common factors \(b^2\) and \(x^2\) from both the numerator and the denominator: \[ \frac{27 b^{2} x^{3}}{63 x^{2} b^{2}} = \frac{27 x}{63} \]

Next, we reduce the fraction \(\frac{27 x}{63}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 9: \[ \frac{27 x}{63} = \frac{27 \div 9 \cdot x}{63 \div 9} = \frac{3 x}{7} \]

Final Answer