Final answer:
To rewrite 5-², take the reciprocal of 5, making it 1/5, and then square it to get 1/25.
Step-by-step explanation:
To rewrite the expression 5-² using the reciprocal of 5 and change the exponent to positive 2, we use the rule for negative exponents which states that x-n = 1/xn. This means that a negative exponent indicates that we should take the reciprocal of the base and then apply the positive exponent.
In this example, the base is 5 and the negative exponent is -2. Therefore, the reciprocal of 5 is 1/5 and applying the positive exponent we get (1/5)². This is equivalent to squaring the reciprocal of 5.
Focusing on Squaring of Exponentials, when we square a number, we multiply it by itself. So, (1/5)² is the same as (1/5) × (1/5), which equals to 1/25.