use the strategy for evaluating a^-m/n

EVALUATE:
25^-3/2

I'm not for sure what the strategy for evaluating a^-m/n is. Can anyone help?!

Certainly! To evaluate a negative exponent expressed as a fraction, we can use the strategy of rewriting the expression as a positive exponent.

To evaluate a^-m/n, we can follow these steps:

1. Start by flipping both the numerator and denominator of the fraction. So, m and n become -m and -n.
a^-m/n turns into a^(-m)/(-n).

2. Apply the reciprocal property of exponents. This property states that a^-b can be rewritten as 1/a^b. So we can rewrite a^(-m) as 1/a^m.
Therefore, a^(-m)/(-n) becomes 1/(a^m * (-n)).

Now, to evaluate the specific expression 25^-3/2, we follow the above steps:

1. Flip the numerator and denominator of the fraction: -3/2 becomes -(-3/2), which simplifies to 3/2.
25^3/2 turns into 25^(3/2).

2. Apply the reciprocal property of exponents: 25^(3/2) becomes 1/25^(3/2).

So, 25^3/2 is equivalent to 1/25^(3/2).

To simplify further, we can rewrite 25 as its prime factorization, which is 5^2: 1/((5^2)^(3/2)).

Next, we apply the property of exponents that states raising a power to a power involves multiplying the exponents: 1/(5^(2*(3/2))).

Simplifying the exponent within the parentheses: 1/(5^(3)).

Finally, evaluating 5^3 gives us the result:

1/125.

Therefore, 25^-3/2 is equal to 1/125.