Can someone give explain for why I can't get this simple math problem correct with this method?

[dentalwhiz]

Simplify: (24x^-2*y^-10)/ (3x^-5*y^4)... I got 8x^3/y^-14, which is wrong. I approached this problem by using the rule of subtracting analogous terms when dividing exponents. I know that negative exponents are equal too 1/n (the way the book approached the problem), but isn't my approach to this problem used correct as well? I may have been studying for too long today; some clarification would be great.

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[smilesandwaves]

check your negative signs: for example, -10 - (4)= -14 --->14

 

[dentalwhiz]

The four in the problem is positive, thus (through my approach) -10 - (4)= -14. Either way, both would be incorrect according to the solution which is: 8x^3/y^14. That is not a typo; they are both positive exponents.

 

[artist2022]

Okay, so when I tried it I got:
24x^-2*y^-10/3x^-5*y^4
24/3 = 8
x^-2/x^-5 = -2 - (-5) = 3 --> x^3
y^-10/y^4 = -10 - (4) = -14 --> y^-14
You get: 8x^3*y^-14 (everything is in the numerator when you do this subtracting method)
Which becomes: 8x^3/y^14
You're doing it right, but when you subtract, remember that anything you're left with is found in the numerator.
Hope this helps.

 

[dentalwhiz]

Okay, so when I tried it I got:
24x^-2*y^-10/3x^-5*y^4
24/3 = 8
x^-2/x^-5 = -2 - (-5) = 3 --> x^3
y^-10/y^4 = -10 - (4) = -14 --> y^-14
You get: 8x^3*y^-14 (everything is in the numerator when you do this subtracting method)
Which becomes: 8x^3/y^14
You're doing it right, but when you subtract, remember that anything you're left with is found in the numerator.
Hope this helps.

THANKS! I'm not sure how I missed that, I was stuck on that problem for a while thinking I had the rule incorrectly applied. Great explanation

 

[DAT Destroyer]

Simplify: (24x^-2*y^-10)/ (3x^-5*y^4)... I got 8x^3/y^-14, which is wrong. I approached this problem by using the rule of subtracting analogous terms when dividing exponents. I know that negative exponents are equal too 1/n (the way the book approached the problem), but isn't my approach to this problem used correct as well? I may have been studying for too long today; some clarification would be great.

yes you did it correctly except for the part that involves the variable y:

y^(-10)/y^4 = y^ (-10-4) = y^(-14) in the numerator. To make the exponent positive, you bring it to the denominator and you get :8x^3/y^14.

here is another example : x^(-3)/x^(4) = x^(-3-4) = x^(-7) = 1/x^(7)