Answer:
[tex]\frac{x^4}{y^2}[/tex]
Step-by-step explanation:
1) Simplify using the order of operations, or PEMDAS. Whenever an exponent is outside of a set of parentheses, distribute it by multiplying that exponent with each of the exponents of the terms within the parentheses. Thus, [tex]x^2[/tex] becomes [tex]x^4[/tex] and [tex]y^-^1[/tex] becomes [tex]y^-^2[/tex].
[tex](x^2y^-^1)^2\\= x^2^(^2^)y^(^-^1^)^(^2^)\\= x^4y^-^2[/tex]
2) Notice that there is a negative exponent, which means we can still simplify further. Whenever there is term with a negative exponent, write the term as its reciprocal (picture it as a fraction, but switch the denominator for the numerator and vice versa) and get rid of the negative sign on the exponent. Then, multiply.
[tex]x^4y^-^2\\= x^4 (\frac{1}{y^2}) \\= \frac{x^4}{y^2}[/tex]
