Question 73984
*[Tex \Large (\frac{-3a^2b}{35a^5})(\frac{14a^3b^2}{-9b^4})]When you multiply identical bases with exponents, you add the exponents (ie *[Tex \Large x^2*x^2=x^{2+2}=x^4] note: bases must be the same).
*[Tex \Large \frac{-42a^{2+3}b^{1+2}}{-315a^{5}b^4}]Multiply the common bases together and the constants together. When you divide bases with exponents, you subtract the exponents (ex *[Tex \Large \frac{x^5}{x^2}=x^{5-2}=x^3]
*[Tex \Large \frac{-42a^{5-5}b^{3-4}}{-315}] Divide identical bases by subtracting exponents.
*[Tex \Large \frac{-42a^0b^{-1}}{-315}]Rewrite *[Tex \Large b^{-1} to \frac{1}{b^1}] and *[Tex \Large a^0] to 1
*[Tex \Large \frac{-42}{-315b}]Reduce the fraction
*[Tex \Large \frac{2}{15b}]Here is the simplified form
<p>
Check:
Let a=1 and b=2
*[Tex \Large (\frac{-3a^2b}{35a^5})(\frac{14a^3b^2}{-9b^4})]
*[Tex \Large (\frac{-3(2)}{35})(\frac{14(2)^2}{-9(2)^4})]Plug in values
*[Tex \Large (\frac{-6}{35})(\frac{56}{-144})]
*[Tex \Large \frac{-336}{-5040}]
*[Tex \Large \frac{1}{15}]
Now lets compare this to our answer
Let a=1 and b=2
*[Tex \Large \frac{2}{15b}]
*[Tex \Large \frac{2}{15(2)}]Plug in values
*[Tex \Large \frac{2}{30}]
*[Tex \Large \frac{1}{15}]
Since these 2 answers are equal, it verifies our answer. Hope this helps.