<p>if a and b are positive integers and (1/a^2 1/b^3) =432, what is the value of ab? a) 6 b)12 c)18 D)24 E) 36</p>
<p>You said 1/a^2 multiplied by 1/b^3 equals 432. If that’s what the question asked, then it’s impossible. (the only solution is a=+/- 1/4 and b=1/3)</p>
<p>well in the explanation it says Choice (B) is correct. Simplifying the exponential part of the expression gives(6/a^2 6/b^3)=(a^3)(b^2)= 432. The prime factorization of 432 is
(3^3)(2^4) so Since a and b must be positive integers, it follows that a^3=3^3 and b^2=2^4=(2^2)^2 This yields a=3 and b=2^2=4. The question asks for the product of a and b which is 3 times 4 =12 </p>
<p>but i dont get it the explanaton …?</p>
<p>oh and i forgot to include that the question say {(1/a^2)(1/b^3)}^6
the whole problem is to the 6th power to equal =432</p>
<p>Ohh, that makes more sense.</p>
<p>First step, you can simplify out the sixth power. Whenever you have an exponent out of the parentheses, you multiply it by each variable on the inside. So (a^(1/2)<em>b^(1/3))^6 equals a^3</em>b^2, since 6<em>1/2=3 and 6</em>1/3=2. Then you take the prime factorization of 432, which is 3<em>3</em>3<em>2</em>2<em>2</em>2. Since you have three 3’s and a^3, a=3. Since you have four 2’s and b^2, b=4. Now all the numbers in the prime factorization are accounted for, so you have 3^3*4^2=432.</p>
<p>Since a=3 and b=4, a*b=12. Choice B is correct.</p>
<p>Sorry if this was confusing, this is the best way I could think of to explain it. >_<</p>
<p>thanks i get it</p>