Question

(3/5)-² .Solve the problem and explain step by step​

Answer 1

To solve (3/5)-², take the reciprocal of 3/5 to get 5/3, and then square it to get 25/9, which is the final answer.

Step-by-step explanation:

The student has asked to solve (3/5)-². This is a mathematical problem involving negative exponents. The rule for negative exponents is that a negative exponent means to take the reciprocal of the base and then apply the exponent.

Let's solve the problem step by step:

1. First, recognize that the negative exponent means we should take the reciprocal of the fraction. The reciprocal of 3/5 is 5/3.
2. Next, apply the exponent of 2 to the reciprocal. So we will square 5/3.
3. When we square the numerator and denominator separately, it becomes (5²)/(3²).
4. The result is 25/9, as 5² = 25 and 3² = 9.

Therefore, the solution to (3/5)-² is 25/9.