Question

Can someone help me on this ? its Algebra 1 on exponents

Answer 1

The volume of a rectangular prism is its length times width times height, or algebraically, $V=lwh$. 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 $l=x, w= \frac{x}{2},h= \frac{x}{3}$ into the formula for volume. You get $(x)( \frac{x}{2})( \frac{x}{3} )$, and you multiply these factors together. As you would with ordinary fractions, multiply the numerators and denominators across. You get $\frac{(x)(x)(x)}{(1)(2)(3)} = \frac{x^3}{6}$. It seems that the book wants you to simplify by bringing the 6 up to the denominator. Recall the rule $x^{-n}= \frac{1}{x^n}$, if n is non-negative. The opposite applies so that $\frac{1}{6} = 6^{-1}$. For your final answer, you write $6^{-1}x^3$. This corresponds to answer choice B.