<p>Please help me with question from CB book</p>
<p>page 596 #8</p>
<p>Thank you</p>
<p>if a and b are positive integers and (a^0,5 b^1/3)^6 =432
What is the value of ab?
a) 6
b) 12
C) 18
d) 24
E)36</p>
<p>Factorize 432 as far as possible, you will find that it equals (2^4)(3^2)</p>
<p>Then ( (a^1/2) (b^1/3))^6 = (a^3) (b^2) = 432 = (2^4)(3^2)</p>
<p>So b = sqrt(2^4) = 4, and a=3;
ab = 12</p>
<p>If I'm not mistaken and the problem is (a^(0.5) * b^(1/3) )^6 = 432</p>
<p>then the answer is 12. --> b</p>
<p>EXPLANATION
first if you factor it out you'd get a ^ 3 * y ^2 = 2^4 * 3^3</p>
<p>The "2^4 * 3^3" can be found by prime factorization of 432.
Now you see that 3^3 corresponds with a^3 and now
you must correspond 2^4 to y^2. And you will find that y = 4 or -4 and since the value has to be positve it's 4.</p>
<p>Hence, 4 * 3 = 12 =)</p>
<p>ok.. how do you do prime factorization???</p>
<p>optimizer dad is wrong</p>
<p>"you will find that it equals (2^4)(3^2)"</p>
<p>no...that's not right. read my explanation</p>
<p>do you have a ti-89? if so then you use teh factor from the f2 menu and type in 432.</p>
<p>otehrwise you can use the old fashioned "hand" method. keeep factoring with primes until you can't anymore...algebra 8th grade?</p>
<p>no ti-89, How do you do it by hand??</p>
<p>432
2 216
2 108
2 54
2 27
3 9
3 3</p>
<p>now you have 3 3's and 4 2's...make sense?</p>
<p>meaning 3 ^ 3 and 2 ^ 4</p>
<p>understand?</p>
<p>in these kind of problems...this is very a calculator can really cut down on time...I solved this ins 30 seconds...with my calc...by hand it would take me atleast 2 min if I got the problem right when I saw it</p>
<p>strange enough my calculator give this to me</p>
<p>2
2
2
2
3
3</p>
<p>not 3 3's........</p>
<p>try again... it should give you 2^4 and 3^3</p>
<p>try out manually 2 * 2 * 2 * 2 * 3 * 3 * 3 = 432</p>
<p>yeah I did it... It was a mistake of mine, I just made a program but put the wrong command in it</p>
<p>nice...good luck =) good to see you created a program...that's the best way to go and well believe or not it's a good way to learn.</p>