(1/5)^2 ÷ _ = (1/5)^(-2)
Answer (1)
To solve the equation x ( 1/5 ) 2 = ( 1/5 ) − 2 , we need to find the value of x that makes this equation true.
First, let's simplify both sides of the equation:
Calculate ( 1/5 ) 2 :
( 1/5 ) 2 = ( 5 1 ) ⋅ ( 5 1 ) = 25 1
Simplify ( 1/5 ) − 2 :
The negative exponent indicates that we take the reciprocal of the base and raise it to the positive exponent:
( 1/5 ) − 2 = ( 5 1 ) − 2 = ( 1 5 ) 2 = 5 2 = 25
So, we have:
x 1/25 = 25
To find x , multiply both sides of the equation by x and then by 25 :
1 = 25 x
Now, solve for x :
x = 25 1
Therefore, the missing value in the division is x = 25 1 .
