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Lena [83]
3 years ago
10

Utilize exponent rules to simplify the following 10x^3y^4 over 4xy^7

Mathematics
1 answer:
wariber [46]3 years ago
7 0
\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\
a^{-{ n}} \implies \cfrac{1}{a^{ n}}
\qquad \qquad
\cfrac{1}{a^{ n}}\implies a^{-{ n}}
\qquad \qquad 
a^{{{  n}}}\implies \cfrac{1}{a^{-{{  n}}}}

so, in short, if you move a factor from the bottom to the top, or the other way around, from the top to the bottom, then you change the sign of the exponent.

\bf \cfrac{10x^3y^4}{4xy^7}\implies \cfrac{10x^3y^4}{4x^1y^7}\implies \cfrac{10}{4}\cdot \cfrac{x^3y^4}{x^1y^7}\implies \cfrac{5}{2}\cdot \cfrac{x^3x^{-1}y^4y^{-7}}{1}
\\\\\\
\cfrac{5}{2}\cdot x^{3-1}y^{4-7}\implies \cfrac{5}{2}x^2y^{-3}\implies \cfrac{5x^2y^{-3}}{2}\implies \cfrac{5x^2}{2y^3}
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