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Simplify expression with laws of indices

dmarley

New member
May 20, 2019
2
Helping my daughter with her math and hit this one and not sure how to advise. All help welcome


(x-2y10)3 / (x-4yz4)-5

This one throws me off because I don't know how to deal with the z, as only on the right side of the divide
 

Wilmer

In Memoriam
Mar 19, 2012
376
Ottawa Ontario Canada
(x-2y10)3 / (x-4yz4)-5
This one throws me off because I don't know how to deal with the z, as only on the right side of the divide
z^(4*(-5)) = z^(-20)
Now move to numerator:
z^(-20) = z^20

So you'll end up with: y^35 * z^20 / x^26
 

topsquark

Well-known member
MHB Math Helper
Aug 30, 2012
1,101
The Astral plane
Helping my daughter with her math and hit this one and not sure how to advise. All help welcome


(x-2y10)3 / (x-4yz4)-5

This one throws me off because I don't know how to deal with the z, as only on the right side of the divide
The basic rule is \(\displaystyle a^{-1} = \dfrac{1}{a}\) and \(\displaystyle \left ( a^{-1} \right ) ^{-1} = a\).

Strategy: Get rid of those pesky negative powers.
\(\displaystyle \dfrac{ \left ( x^{-2}y^{10} \right ) ^3 }{ \left ( x^{-4} y z^4 \right ) ^{-5} }\)

\(\displaystyle = \left ( x^{-2}y^{10} \right ) ^3 \left ( x^{-4} y z^4 \right ) ^5\)

\(\displaystyle = \left ( \dfrac{y^{10}}{x^2} \right ) ^3 \left ( \dfrac{yz^4}{x^4} \right ) ^5\)

Can you finish?

-Dan
 

dmarley

New member
May 20, 2019
2
topsquark - thanks for the help

following your basic rule really helped out and clarified for us.