# Simplify expression with laws of indices

• MHB
• dmarley
In summary, the user was struggling with a math problem involving negative powers and was unsure how to proceed. Another user provided a strategy to get rid of the negative powers by using the rule a^-1 = 1/a. The final solution involved simplifying the expression and resulted in y^35 * z^20 / x^26. The user thanked the helper for their assistance.

#### dmarley

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

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 $$\displaystyle a^{-1} = \dfrac{1}{a}$$ 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

topsquark - thanks for the help

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