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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)

1 Answer

3 votes

Answer:


\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)}

User Jeff Davenport
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