The volume of a rectangular prism is its length times width times height, or algebraically, [tex]V=lwh[/tex]. You may be used to computing volume with numbers, but remember, a variable is a stand-in for a number. So you can solve this in the same way. Substitute [tex]l=x, w= \frac{x}{2},h= \frac{x}{3} [/tex] into the formula for volume. You get [tex](x)( \frac{x}{2})( \frac{x}{3} )[/tex], and you multiply these factors together. As you would with ordinary fractions, multiply the numerators and denominators across. You get [tex] \frac{(x)(x)(x)}{(1)(2)(3)} = \frac{x^3}{6} [/tex]. It seems that the book wants you to simplify by bringing the 6 up to the denominator. Recall the rule [tex]x^{-n}= \frac{1}{x^n} [/tex], if n is non-negative. The opposite applies so that [tex] \frac{1}{6} = 6^{-1}[/tex]. For your final answer, you write [tex]6^{-1}x^3[/tex]. This corresponds to answer choice B.
