multiply: (-3a^2 b / 35 a^5) x (14 a^3 b^2 / -9 b^4)

[jburgswife30]

(-3a^2 b / 35 a^5) x (14 a^3 b^2 / -9 b^4)

= (-3 a^2 b * 14 a^3 a^3 b^2) * (35 a^5 * 9 b^4)

= -42 / -315

this is where I'm stuck

 

[soroban]

Re: multiply rational expression

Hello, jburgswife30!

\(\displaystyle \L\frac{-3a^2b}{35a^5} \,\cdot\, \frac{14a^3b^2}{-9b^4} \;= \;\frac{-3a^2b\,\cdot14a^3a^3b^2}{35a^5\,\cdot\,9b^4} \;=\;\frac{-42}{-315}\;\) . . . This is wrong

You're stuck on the arithmetic?


We have: \(\displaystyle \L\:\frac{-3a^2b}{35a^5}\,\cdot\,\frac{14a^3b^2}{-9b^4}\)

Make one fraction: \(\displaystyle \L\:\frac{(-3)(14)a^2\cdot a^3\cdot b\cdot b^2}{(35)(-9)a^5b^4}\)

. . and we have: \(\displaystyle \L\:\frac{-42a^5b^3}{-315a^5b^4} \;=\;\frac{-42}{-315b}\)


"Negative divided by negative" is "positive"
. . so we have: \(\displaystyle \L\:\frac{42}{315b}\)

Now reduce the fraction!

 

[galactus]

\(\displaystyle \L\\\frac{-3a^{2}b}{35a^{5}}\cdot\frac{14a^{3}b^{2}}{-9b^{4}}\)


\(\displaystyle \L\\\frac{\sout{-42}^{2}\not{a^{5}}\not{b^{3}}}{\sout{-315}^{15}\not{a^{5}}b^{\not{4}}^{1}\)

\(\displaystyle \L\\\frac{2}{15b}\)