Question

Look at image shown simplify expression and write answer without negative exponents please

Answer 1

The expression without a negative exponent will be:

`(8x^(-4)y^(-8))/(-2xy^5)=-(4)/(x^5y^(13))`

Explanation:

Given the function

`(8x^(-4)\:y^(-8))/(-2xy^5)`

`\mathrm{Apply\:the\:fraction\:rule}:\quad (a)/(-b)=-(a)/(b)`

`(8x^(-4)\:y^(-8))/(-2xy^5)=-(8x^(-4)y^(-8))/(2xy^5)\\`

`\mathrm{Divide\:the\:numbers:}\:(8)/(2)=4`

`=-(4x^(-4)y^(-8))/(xy^5)`

`\mathrm{Apply\:exponent\:rule}:\quad (x^a)/(x^b)=(1)/(x^(b-a))`

`=-(4y^(-8))/(x^5y^5)`

`\mathrm{Apply\:exponent\:rule}:\quad (x^a)/(x^b)=(1)/(x^(b-a))`

i.e.
`(y^(-8))/(y^5)=(1)/(y^(5-\left(-8\right)))`

so the expression becomes

`(8x^(-4)\:y^(-8))/(-2xy^5)=-(4)/(x^5y^(5-\left(-8\right)))`

`=-(4)/(x^5y^(13))`

Therefore, the expression without a negative exponent will be:

`(8x^(-4)y^(-8))/(-2xy^5)=-(4)/(x^5y^(13))`