Questions: 14/7a^3 = /14a^3b^2 14/7a^3 = square/14a^3b^2

Solution Steps

To rewrite the given rational expression with a new denominator, we need to determine what factor is missing in the original denominator to make it equal to the new denominator. Once identified, multiply both the numerator and the denominator of the original expression by this factor to obtain the equivalent expression.

To solve the given problem, we need to rewrite the rational expression \(\frac{14}{7a^3}\) as an equivalent rational expression with the denominator \(14a^3b^2\).

The original rational expression is: \[ \frac{14}{7a^3} \]

The new denominator we want is: \[ 14a^3b^2 \]

To convert the original denominator \(7a^3\) to the new denominator \(14a^3b^2\), we need to find the factor by which we multiply \(7a^3\) to get \(14a^3b^2\).

First, compare the coefficients:

• The original coefficient is 7, and the new coefficient is 14. Thus, the multiplicative factor for the coefficient is \(\frac{14}{7} = 2\).

Next, compare the variables:

• The original denominator has \(a^3\), and the new denominator also has \(a^3\), so no additional factor is needed for \(a\).
• The new denominator has \(b^2\), which is not present in the original denominator. Therefore, we need to multiply by \(b^2\).

Thus, the overall multiplicative factor is \(2b^2\).

Multiply both the numerator and the denominator of the original expression by the factor \(2b^2\) to obtain the equivalent expression: \[ \frac{14 \times 2b^2}{7a^3 \times 2b^2} = \frac{28b^2}{14a^3b^2} \]

Final Answer