Given the expression:
[tex]-5y^2\cdot5y^2\cdot5y^2\cdot5y^2[/tex]You need to apply the Product of Powers Property, which states that:
[tex]b^m\cdot b^n=b^{m+n}[/tex]Then, you can add the exponents of the same base "y".
Notice that 5 is repeated 4 times. Therefore, you can rewrite the expression as follows:
[tex]=-(5y^{2+2+2+2})[/tex][tex]=-(5y^8)[/tex]According to the Power of a Power Property:
[tex](b^m)^n=b^{mn}[/tex]Therefore, you can rewrite the expression using that property:
[tex]=-(5y^2)^4[/tex]Hence, the answer is: Option A.