system

 

One ordered pair (a,b) satisfies the two equations ab^4 = 48 and ab = 72. What is the value of b in this ordered pair?   

 

To find b, consider                                                  ab⁴  =  48  

 

We will divide both sides of that by ab.  

 

Since ab=72, we will divide the left side  

by "ab" and the right side by its equal 72.  

                                                                              ab⁴         48  

                                                                             ——   =   ——  

                                                                              ab           72  

Note that ab⁴ = (ab) * (b³)  

 

Cancel ab out of the left side.  

Reduce 48/72 on the right side.  

                                                                               b³           2  

                                                                             ——   =   ——  

                                                                                1            3  

 

 

                                                                                 b   =   cube root of (2 / 3)  

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\(cuberoot(2/3)\)

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