<p>Would someone explain a fairly quick/easy/effective way to solve these problems?</p>
<p>College Board blue book practice test #4 section 4 page 596</p>
<p>Question 8:</p>
<p>If a and b are positive integers and (a^(1/2) x b^(1/3))^6 = 432, what is the value of ab?</p>
<p>A)6
B) 12
C) 18
d) 24
E) 36</p>
<p>Practice test #7 section 5 page 796</p>
<p>Question 16 (there's a diagram involved, so I won't write out the question here...)</p>
<p>Thank you all very much in advance!!!</p>
<p>Question 8 seems awfully difficult for only question 8.</p>
<p>You can expand it and get a^3 x b^2 = 432, but it's not easy to get from there to ab. The prime factorization of 432 is 2x2x2x2x3x3x3, so you can group the 3's up and cube them. 3^3 = 3x3x3. What squared equals 2x2x2x2? 4^2 = 2x2x2x2. So a is 4 and b is 3. The answer is B).</p>
<p>If you re-factor, you get</p>
<pre><code> (ab)(ab)a= 432
</code></pre>
<p>in which case it is obvious that ab= 6 is too low and ab >= 18 is too high. Process of elimination, then, settles on (B) quickly.</p>