simplifying a fraction with variables with negative exponent

[brynnpet]

This is my question:

in a problem like this...5 x squared divided by 10 x to the negative 5th power- how do i simplify this?

i think you say x squared minus x to the negative 5th = x to the 7th and the answer is 1/2 x to the 7th

my mom suggests that the rule does not apply for variables with negative integers- she thinks we must invert the x to the negative 5th and solve.

please give me some guidance on how to simplify this problem.

b- 6th grade student in florida

 

[Deleted member 4993]

This is my question:

in a problem like this...5 x squared divided by 10 x to the negative 5th power- how do i simplify this?

i think you say x squared minus x to the negative 5th = x to the 7th and the answer is 1/2 x to the 7th <<<< You are correct

my mom suggests that the rule does not apply for variables with negative integers- she thinks we must invert the x to the negative 5th and solve.

please give me some guidance on how to simplify this problem.

b- 6th grade student in florida

\(\displaystyle \frac{5x^2}{10x^{-5}} = \frac{1}{2}x^{2-(-5)} = \frac{1}{2}x^{7}\)

 

[barson90]

I hope this won't confuse you, but another way to think about this is that if the ENTIRE denominator is raised to a negative power, then you can move it to the numerator and make the exponent positive. (Since we can factor out (1/2), we're left with x^(-5). So, the numerator becomes x^2 times x^5. When multiplying likes bases, in this case "x" , add the exponents. So, we have x^(2+5) = x^7