Question

Nadine and Calvin are simplifying the expression

Answer 1

Answer: Calvin result is correct

First it is necessary to state clear the following rules:

-The multiplication of exponents of the same base is equal to the same base raised to the sum of the exponents.

-The quotient or division of exponents of the same base is equal to the same base raised to the subtraction of the exponents.

On the other hand:

If a positive number is multiplied by a negative number, the result has a negative sign. In addition, if two numbers with equal signs are multiplied, the result has a positive sign. In the same way it happens with the division.

Knowing this, let's try the first step in simplifying according to Calvin:

`{((r^(-5)s^(-3))/(r^(8)s^(-2)))}^(-4)`

`{(r^(-5-8)s^(-3-(-2)))}^(-4)` (1)

`{(r^(-13)s^(-1))}^(-4)` (2)

`r^(52)s^(4)` (3)>>>>This is the final result

Now, lets try according to Nadine:

`{((r^(-5)s^(-3))/(r^(8)s^(-2)))}^(-4)`

`(r^(20)s^(12))/(r^(-32)s^(8))` (4)

As we can see this results differs from the result Nadine had, but if we continue we will get the same correct result as equation (3):

`r^(20-(-32))s^(12-8)=r^(52)s^(4)` (5)

This means, Calvine's and Nadine's first proposed steps are correct, but Calvine's result is correct.

If Nadine had followed the rules explained above, the result would had been correct, as well.