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Novay_Z [31]
3 years ago
12

If the area of a rectangle is 24a^2b and the length is 8ab^2, what would be the width of the rectangle, given that width is foun

d by dividing area by length? Simplify the answer. 1. 3a/b 2. b/3a 3. 3/ab 4. 3ab
Mathematics
1 answer:
tester [92]3 years ago
5 0
\bf ~~~~~~~~~~~~\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}}
\\\\
-------------------------------

\bf \textit{area of a rectangle}\\\\
A=WL~~
\begin{cases}
W=width\\
L=length\\
-----\\
A=24a^2b\\
L=8ab^2
\end{cases}\implies 24a^2b=W(8ab^2)\implies \cfrac{24a^2b}{8ab^2}=W
\\\\\\
\cfrac{24}{8}\cdot \cfrac{a^2b}{ab^2}=W\implies 3\cdot \cfrac{a^2a^{-1}}{b^2b^{-1}}=W\implies 3\cdot \cfrac{a^{2-1}}{b^{2-1}}=W\implies \cfrac{3a}{b}=W
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