Question

Simplify the expression.

Answer 1

`(x^4)/(y^2)`

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,
`x^2` becomes
`x^4` and
`y^-^1` becomes
`y^-^2`.

`(x^2y^-^1)^2\\= x^2^(^2^)y^(^-^1^)^(^2^)\\= x^4y^-^2`

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.

`x^4y^-^2\\= x^4 ((1)/(y^2)) \\= (x^4)/(y^2)`