Or a slightly different explanation. You had this:
49<SUP>y</SUP> = 1/7
We know that 1/7 can be written as 7<SUP>-1</SUP> by using the definition of a negative exponent. Now we have
49<SUP>y</SUP> = 7<SUP>-1</SUP>
Can we write 49 as a power of 7? Sure! 49 = 7<SUP>2</SUP>. So,
(7<SUP>2</SUP>)<SUP>y</SUP> = 7<SUP>-1</SUP>
When you raise a power to a power, you multiply the exponents. So,
7<SUP>2y</SUP> = 7<SUP>-1</SUP>
Since the bases are the same, and the expressions are equal, the exponents must be equal as well:
2y = -1
y = -1/2