Question

Simplify
6x^4 y^-5 z^6 / 2x^-2 z^-7
Write your answer using only positive exponents

Answer 1

\(\bf \cfrac{6x^4y^{-5}z^6}{2x^{-2}z^{-7}}\implies \cfrac{6x^4}{1}\cdot \cfrac{1}{2x^{-2}}\cdot \cfrac{y^{-5}}{1}\cdot \cfrac{1}{z^{-7}}\cdot \cfrac{z^6}{1}
\\ \quad \\
\textit{bear in mind }\qquad a^{-{\color{red} n}} \implies \cfrac{1}{a^{\color{red} n}}\qquad \qquad

\cfrac{1}{a^{\color{red} n}}\implies a^{-{\color{red} n}}
\\ \quad \\
% negative exponential denominator
a^{{\color{red} n}} \implies \cfrac{1}{a^{-\color{red} n}}
\qquad \qquad

\cfrac{1}{a^{-\color{red} n}}\implies \cfrac{1}{\frac{1}{a^{\color{red} n}}}\implies a^{{\color{red} n}} \)

what do you think?

Answer 2

\[\frac{ 6x^{4}y^{-5}z^{-6} }{ 2x^{-2}z^{-7} }\]
flip negatives
\[\frac{ 6x^{4}x^{2}z^{6}z^{7} }{2y^{5} }\]
combine exponents
\[\frac{ 6x^{6}z^{13} }{ 2y^{5} }\]
simplify fraction
\[\frac{ 3x^{6}z^{13} }{y^{5} }\]

Answer 3

\(\large \bf {\cfrac{6x^4y^{-5}z^6}{2x^{-2}z^{-7}}\implies \cfrac{6x^4}{1}\cdot\cfrac{1}{2} \cdot \cfrac{1}{x^{-2}}\cdot \cfrac{y^{-5}}{1}\cdot \cfrac{1}{z^{-7}}\cdot \cfrac{z^6}{1}
}\)
may look better

Answer 4

wouldnt it be 3x^6z^7 / y^5z^6 ?

Answer 5

yes, I missed the negative on the Z, you're correct

Answer 6

thanks

Answer 7

wait your original equation had a positive z exponent on top, if that's the case then the answer i gave is correct

Answer 8

ur right. i just realized when you typed it you put a negative by mistake.