(x^3*y^3)*(x^4*y^a)=x^7 what is a

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Using the properties of powers (see the Formulary) and collecting like terms together:

x³*y³*x⁴*y^a = x⁷y^3-a  

If this is to equal x⁷ then the y term must equal 1.  Now y⁰ = 1 so we must have 3-a = 0, or a =3

I believe you made a small mistake Alan.  It is 3+a

$$x^3y^3x^4y^a=x^7\\ x^7y^{3+a}=x^7\\ y^{3+a}=1\\ y^{3+a}=y^0\\ 3+a=0\\ a=\: -3\\$$

Oops!