10 to the power 2y = 25

When given the equation 10 to the power 2y = 25, we can solve for the value of y and then find the value of 10 to the power -y.

Solving for y:
To find the value of y, we need to isolate the variable. We can do this by taking the logarithm of both sides of the equation. In this case, we will use the logarithm base 10 (also known as the common logarithm) since we have 10 as the base in the equation.

Logarithm of both sides:
log (10 to the power 2y) = log 25

Applying the logarithmic property:
2y * log 10 = log 25

Simplifying:
2y * 1 = log 25

Therefore:
2y = log 25

Dividing by 2:
y = (log 25) / 2

Calculating the value of y:
Using a calculator, we find that log 25 is approximately 1.3979. Therefore, y is equal to (1.3979) / 2, which is approximately 0.6989.

10 to the power -y:
Now that we have found the value of y, we can substitute it back into the equation 10 to the power -y to find the result.

Substituting y = 0.6989:
10 to the power -y = 10 to the power -(0.6989)

Using the property of exponents:
10 to the power -(0.6989) = 1 / (10 to the power 0.6989)

Calculating the value:
Using a calculator, we find that 10 to the power 0.6989 is approximately 4.1246. Therefore, 1 / (10 to the power 0.6989) is approximately 0.2417.

Conclusion:
Therefore, 10 to the power minus y is approximately 0.2417.