Question

If 10^2y = 25 then 10^-y equals

Answer 1

Step-by-step explanation:

To solve this problem, you could first solve for y and then plug that value into 10-y. But since the question doesn't ask us to solve for y, it would be easier to manipulate the original equation 102y = 25 using exponent rules until the lefthand side reads 10-y.

102y = 25

(102y)-1/2= 25-1/2

Recall that when we raise an exponential expression to another exponent, we multiply the exponent values together. In this case, when we multiply 2y*(-1/2) we end up with -y. So now we have:

10-y = 25-1/2

Now, let's rewrite the righthand side so we can simplify it. Recall that x-1 = 1/x and that x1/2 = sqrt(x).

10-y = 1/(251/2)

10-y = 1/sqrt(25)

10-y = 1/5