<p>Post any questions here :)</p>
<p>(a^(1/2) * b^(1/3) ) ^6 = 432</p>
<p>what is the value of ab?</p>
<p>couldnt find an easy way to do this so what i did was a^3 * b^2 = 432, and just plugged in a random number for a, solved for b, and looked through the 5 solutions… is there another way to solve this?</p>
<p>The first thing I thought of was logarithms, but they’re not used in the SAT I and I’m not sure it’d even work in this situation. The easiest way to solve this question is to expand the exponent, making the equation: a^3.b^2 = 432, then prime factorize 432. This gives you a^3.b^2 = 3^3.2^4, which is effectively a^3.b^2=3^3.(2^2)^2 so a=3 and b=4.</p>
<p>Yea, that fastest way is just to plug the answer choices in. But cross out any answer choice that doesn’t have a multiple of two. </p>
<p>As Jimmy797 said, just break 432 down into its factors… 432 is an even number, it is divisible by 2, which makes 2*216.</p>
<p>If you double the 2, and halve the 216, you get 4*108.</p>
<p>Do this again and you get 8*54.</p>
<p>And then 16*27.
There for, a=3,b=4</p>
<p>is 0 even?</p>
<p>and to confirm…
0 is an integer
prime numbers start at 2</p>
<p>0 is even. And yes to both.</p>