Answer: The required GCF is 14fg².
Step-by-step explanation: We are given to determine the gcf of the following two expressions :
[tex]E_1=56f^3g^2,\\\\E_2=70fg^3.[/tex]
We can write the given expressions in factored form as follows :
[tex]E_1=56f^3g^2=2\times2\times2\times7\times f\times f\times f\timesg\times g,\\\\E_2=70fg^3=2\times5\times7\timesf\times g\times g\times g.[/tex]
Therefore, the GCF(greatest common factor) of the given expressions is
[tex]GCF(E_1,E_2)=2\times7\times f\times g\times g=14fg^2.[/tex]
Thus, the required GCF is 14fg².
