Questions on Algebra: Exponents and operations on exponents answered by real tutors!

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Question 169632: simplify (x-2y8z)-5
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(x-4y9z)-4
Numbers are all exponents: simplify (x-2y8z)-5
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(x-4y9z)-4
Numbers are all exponents
Answer by jim_thompson5910(9897) About Me  (Show Source):
You can put this solution on YOUR website!
Note:

(x^(-2)y^(8)z)^(-5)=1/(x^(-2)y^(8)z)^5


and


1/(x^(-4)y^(9)z)^(-4)=(x^(-4)y^(9)z)^(4)


In other words, we just flip the fractions


So

((x^(-2)y^(8)z)^(-5))/((x^(-4)y^(9)z)^(-4)) becomes



((x^(-4)y^(9)z)^(4))/((x^(-2)y^(8)z)^5)


(x^(-4*4)y^(9*4)z^(1*4))/(x^(-2*5)y^(8*5)z^(1*5)) Distribute the exponents.


(x^(-16)y^(36)z^(4))/(x^(-10)y^(40)z^(5)) Multiply the exponents.


x^(-16--10)y^(36-40)z^(4-5) Subtract the exponents


For example, (x^(-16))/(x^(-10))=x^(-16--10)


x^(-16+10)y^(36-40)z^(4-5) Simplify


x^(-6)y^(-4)z^(-1) Combine the exponents.


(1/x^(6))(1/y^(4))(1/z^(1)) Flip the variables with negative exponents.


1/(x^6y^4z^1) Combine the fractions.


1/(x^6y^4z) Simplify


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Answer:


So ((x^(-2)y^(8)z)^(-5))/((x^(-4)y^(9)z)^(-4)) simplifies to 1/(x^6y^4z)


In other words, ((x^(-2)y^(8)z)^(-5))/((x^(-4)y^(9)z)^(-4))=1/(x^6y^4z) where no variables can be equal to zero.