The first step for finding out whether or not this expression is equivalent to [tex] \sqrt{4} [/tex] is to reduce the fraction with [tex] x^{7} [/tex]. You can begin to do this by dividing the terms with the same base by subtracting their exponents.
[tex] \frac{16 x^{11-7} y^{8} }{81 y^{6} } [/tex]
Subtract the exponents.
[tex] \frac{16 x^{4} y^{8} }{81 y^{6} } [/tex]
Now reduce the fraction with [tex] y^{6} [/tex] by doing the same process. Since I just showed you how to do this,, I will skip over this.
[tex] \frac{16 x^{4} y^{2} }{81} [/tex]
Since we cannot simplify this expression any further,, your answer is going to be [tex] \frac{16 x^{4} y^{2} }{81} [/tex],, which is not equivalent to [tex] \sqrt{4} [/tex].
Let me know if you have any further questions.
:)
