Simply: Please show me how to work the problems. (7/2)^-3
(a/b)^(-n) = (b/a)^(+n)
so
(7/2)^-3 = (2/7)^3
= 8/343
To solve the problem (7/2)^-3, we need to understand the process of working with negative exponents and the rules of exponentiation.
Step 1: Understanding Negative Exponents
When we have a negative exponent, it means that the base should be moved to the opposite location in the fraction. For example, a^-n is equivalent to 1/a^n. It's useful to remember that a negative exponent signifies taking the reciprocal of the base.
Step 2: Applying the Rule of Negative Exponents
In the given problem, we have (7/2)^-3. According to the rule of negative exponents, we need to take the reciprocal of the base and change the sign of the exponent.
Step 3: Reciprocating the Base and Changing the Sign
Using the rule, we can rewrite (7/2)^-3 as (2/7)^3.
Step 4: Evaluating the Exponent
Now that we have transformed the negative exponent into a positive exponent, we can compute the value of (2/7)^3. To do this, we multiply the base, 2/7, by itself three times.
(2/7)^3 = (2/7) * (2/7) * (2/7) = 8/343
So, (7/2)^-3 is equal to 8/343.
In summary, to work the problem (7/2)^-3, you need to follow these steps:
1. Understand the concept of negative exponents.
2. Apply the rule of negative exponents to rewrite the expression.
3. Reciprocate the base and change the sign of the exponent.
4. Evaluate the exponent by multiplying the base three times.
5. Simplify the final fraction, if necessary.
Remember, these steps can also be applied to other problems involving negative exponents.