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]

There are two types of array.

One Dimensional Array

Syntax for default values:

int[] num = new int[5];

Or (less preferred)

int num[] = new int[5];

Syntax with values given (variable/field initialization):

int[] num = {1,2,3,4,5};

Or (less preferred)

int num[] = {1, 2, 3, 4, 5};

Note: For convenience int[] num is preferable because it clearly tells that you are talking here about array. Otherwise no difference. Not at all.

Multidimensional array

Declaration

int[][] num = new int[5][2];

Or

int num[][] = new int[5][2];

Or

int[] num[] = new int[5][2];

Initialization

 num[0][0]=1;
 num[0][1]=2;
 num[1][0]=1;
 num[1][1]=2;
 num[2][0]=1;
 num[2][1]=2;
 num[3][0]=1;
 num[3][1]=2;
 num[4][0]=1;
 num[4][1]=2;

Or

 int[][] num={ {1,2}, {1,2}, {1,2}, {1,2}, {1,2} };

Ragged Array (or Non-rectangular Array)

 int[][] num = new int[5][];
 num[0] = new int[1];
 num[1] = new int[5];
 num[2] = new int[2];
 num[3] = new int[3];

So here we are defining columns explicitly.
Another Way:

int[][] num={ {1}, {1,2}, {1,2,3,4,5}, {1,2}, {1,2,3} };

For Accessing:

for (int i=0; i<(num.length); i++ ) {
    for (int j=0;j<num[i].length;j++)
        System.out.println(num[i][j]);
}

Alternatively:

for (int[] a : num) {
  for (int i : a) {
    System.out.println(i);
  }
}

Ragged arrays are multidimensional arrays.
For explanation see multidimensional array detail at the official java tutorials

try

String[][] arrays = new String[5][];