Quotient Power rules

[Pencil]

First off, I'd like to begin by saying, I know the quotient rule for exponents. You basically subtract the exponents with the same base, but the problems I've done (shown below) seems to smash this rule. I just need some clarity as to what's going on because these problems just doesn't seem to respect the rule. Thanks in advance.

Problem 1:

W^3 X^6 / W^3 X^-4

Answer : X^10

My Approach:

W^3 X^6 / W^3 X^-4

= X^-4 - X^6

= X^2

---------------------------------------------------------


Problem: 2

6 * 10^3 / 8 * 10^6

Answer: 7.5 x 10^-4

My Approach:

6 * 10^3 / 8 * 10^6

= 0.75 X 10^-3 (I simply divided 6 by 8 and subtracted the exponents)

 

[stapel]

Problem 1:

W^3 X^6 / W^3 X^-4

Answer : X^10

My Approach:

W^3 X^6 / W^3 X^-4

= X^-4 - X^6

How did the division of X⁶ by X^-4 turn into a subtraction of X⁶ from X^-4? And doesn't the Quotient Rule for exponents say that you're supposed to subtract the powers, rather than the terms?

 

[lookagain]

First off, I'd like to begin by saying, I know the quotient rule for exponents. You basically subtract the exponents with the same base, but the problems I've done (shown below) seems to smash this rule. I just need some clarity as to what's going on because these problems just doesn't seem to respect the rule. Thanks in advance.

Problem 1:

(W^3 X^6)/(W^3 X^-4)

Answer : X^10

My Approach:

(W^3 X^6)/(W^3 X^-4)

= X^-4 - X^6 \(\displaystyle \ \ \ \ \) As others have pointed out, this is incorrect.

= X^2

---------------------------------------------------------


Problem: 2

6 * 10^3 / 8 * 10^6

Answer: 7.5 x 10^-4

My Approach:

6 * 10^3 /( 8 * 10^6)

= 0.75 X 10^-3 (I simply divided 6 by 8 and subtracted the exponents)\(\displaystyle \ \ \ \ \)And you need to go further after this step.

.

Pencil,

make sure you use grouping symbols