MHB Simplify expression with laws of indices

AI Thread Summary
The discussion revolves around simplifying the expression (x-2y10)3 / (x-4yz4)-5 using the laws of indices. The main challenge is managing the z variable, which only appears in the denominator. By applying the rule for negative powers, z^(-20) is transformed into z^20 in the numerator. The final simplified expression is y^35 * z^20 / x^26. The conversation highlights the importance of understanding negative exponents and their manipulation in algebraic expressions.
dmarley
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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
 
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dmarley said:
(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
 
dmarley said:
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 [math]a^{-1} = \dfrac{1}{a}[/math] and [math]\left ( a^{-1} \right ) ^{-1} = a[/math].

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

[math]= \left ( x^{-2}y^{10} \right ) ^3 \left ( x^{-4} y z^4 \right ) ^5[/math]

[math]= \left ( \dfrac{y^{10}}{x^2} \right ) ^3 \left ( \dfrac{yz^4}{x^4} \right ) ^5[/math]

Can you finish?

-Dan
 
topsquark - thanks for the help

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