Question

Simplify the following questions using the rules for exponents.

Write your answer without negative exponents.


`(9x^(-1) y^(6))/(3x^(-2) y^(-9) )`



`(-6a^(7) b^(8) )/(-3a^(5) b^(7) )`



`((a^(-2) b^(-8) )/(a^(6) b^(4) ) )^(1/2)`

Answer 1

`\frac{9x^(-1)y^6}{3x^(-2)y{-9}}=3xy^(15)\\\\(-6a^7b^8)/(-3a^5b^7)=2a^2b\\\\((a^(-2)b^(-8))/(a^6b^4))^{(1)/(2)}=(1)/(a^4b^6)`

Explanation:

`(9x^(-1)y^6)/(3x^(-2)y^(-9))`

Multiply numerator and denominator by
`x^2y^9`

`(9x^(-1)y^6)/(3x^(-2)y^(-9))* (x^2y^2)/(x^2y^2)=(9xy^(15))/(3x^0y^o)=3xy^(15)`

`(-6a^7b^8)/(-3a^5b^7)`

multiply numerator and denominator by
`a^(-5)b^(-7)`

`(-6a^7b^8)/(-3a^5b^7)* (a^(-5)b^(-7))/(a^(-5)b^(-7))=(-6a^(7-5)b^(8-7))/(-3a^(5-5)b^(7-7))=2a^2b\\\\\\\\((a^(-2)b^(-8))/(a^6b^4))^{(1)/(2)}=\frac{a^{(-2)/(2)}b^{(-8)/(2)}}{a^{(6)/(2)}b^{(4)/(2)}}=(a^(-1)b^(-4))/(a^3b^2)`

Multiply numerator and denominator by
`a^1b^4`

`(a^(-1)b^(-4))/(a^3b^2) * (ab^4)/(ab^4)=(a^0b^0)/(a^4b^6)=(1)/(a^2b^6)}`