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One ordered pair \((a, b)\) satisfies the two equations \(ab^4=384\) and \(a^2b^5=4608\). What is the value of \(a\) in this ordered pair?

 Jul 9, 2020
 #1
avatar+252 
0

This is the concept of algebra, given that ab^4=12 and a^5b^5=7776, the value if a will be found as follows:
ab^4=12
a=12/b^4
also;
a^5=7776/b^5
thus;
a=(7776/b^5)^(1/5)
a=6/b
thus the value of a will be:
6/b=12/b^4
dividing both sides by b we get:
6=12/b^3
multiplying both sides by b^3 we get
6b^3=12
b^3=2
hence;
b=2^(1/3)

 

I'm pretty surre I already answered this...

 Jul 9, 2020
 #2
avatar+252 
0

Oops srry nvm 

MathWizPro  Jul 9, 2020
 #3
avatar+359 
+5

yea, sorry, I accidentally typed it wrong last time

iamhappy  Jul 9, 2020
 #4
avatar+30920 
+3

Like so:

 

 Jul 9, 2020

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