how many times as great is 7^-2 as 7^6

When multiplying two of the same number (with varying powers), simply add the powers together:

A^x * A^y = A^x+y

Inversely, when dividing, subtract the powers:

A^x / A^y = A^x-y

 

To find how many times greater something is, you divide the number you are checking with the number you are comparing it to. So in this case, you will want 7^-2 / 7⁶ to see how many times greater 7² is of 7⁶

Using the above rules of multiplying/dividing powers, this equation is:

7^-2 / 7⁶ = 7^{(-2 - 6)} = 7^-8 = 0.0000001734665256