One ordered pair (a,b) satisfies the two equations \(ab^4 = 12 \) and a^5b^5=7776. What is the value of a in this ordered pair?

Sorry, one is in LaTex. NEED HELP PLEASE

Web2.0CalcUser123
Oct 13, 2018

#1**+3 **

\(ab^4 = 12,~a^5b^5=7776 \\ \text{we want to get rid of }b \text{ by dividing a power of the first equation by a power of the 2nd}\\ \dfrac{(ab^4)^5}{(a^5b^5)^4}=\dfrac{(12)^5}{(7776)^4} \\ \dfrac{a^5b^{20}}{a^{20}b^{20}} = \dfrac{1}{a^{15}} = \dfrac{(2^23)^5}{(2^53^5)^4}=\dfrac{2^{10}3^5}{2^{20}3^{20}}=\dfrac{1}{2^{10}3^{15}}\\ a = (2^{10}3^{15})^{1/15} = 2^{2/3}3\)

Rom
Oct 13, 2018