All methods above you referred is inherited from Object. Object in Java API is an object too. Every class you createed ended with .java is by default inherited from Object. Of course even though an array is an object, and Every thing is an object

It seams you are making a recursive method because you call your method in the return return powArray(a);, so this will call your method again and again until your condition is wrong and return -1.

... i need to write a method called powArray that takes a double array, a, and returns a new array

The first part is correct method called powArray that takes a double array, but the second is not return an array it return a double, instead your method signature should look like :

public static double[] powArray (double a[]){
//------------------^^

Now the return part should be like so ;

public static double[] powArray (double a[]){
    for (int i = 0; i < a.length; i++) {
         a[i] = Math.pow(a[i], 2.0);
    }
    return a;//<<-------------return the result
}

Test

If you try to make this call in your main method :

public static void main(String[] args) {
    double[] a = new double[]{5, 6, 8, 7};
    System.out.println(Arrays.toString(powArray(a)));
}

The output :

[25.0, 36.0, 64.0, 49.0]