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 7a314 as an equivalent rational expression with the denominator 14a3b2.
Step 1: Identify the Original Expression
The original rational expression is:
7a314
Step 2: Identify the New Denominator
The new denominator we want is:
14a3b2
Step 3: Determine the Multiplicative Factor
To convert the original denominator 7a3 to the new denominator 14a3b2, we need to find the factor by which we multiply 7a3 to get 14a3b2.
First, compare the coefficients:
The original coefficient is 7, and the new coefficient is 14. Thus, the multiplicative factor for the coefficient is 714=2.
Next, compare the variables:
The original denominator has a3, and the new denominator also has a3, so no additional factor is needed for a.
The new denominator has b2, which is not present in the original denominator. Therefore, we need to multiply by b2.
Thus, the overall multiplicative factor is 2b2.
Step 4: Multiply the Numerator and Denominator
Multiply both the numerator and the denominator of the original expression by the factor 2b2 to obtain the equivalent expression:
7a3×2b214×2b2=14a3b228b2
Final Answer
The equivalent rational expression is:
14a3b228b2