Video Transcript
Find an expression for the volume
of the given cube whose side lengths are two 𝑥 over five.
We begin by recalling that the
volume of a cube is given by the cube of its side length. This means that if a cube has side
length 𝑙, then its volume is 𝑙 multiplied by 𝑙 multiplied by 𝑙, which is 𝑙
cubed. In this question, we are told that
the side length is two 𝑥 over five. This means that its volume is given
by the expression two 𝑥 over five cubed. Recalling that for any rational
number 𝑎 over 𝑏 and any integer 𝑛 𝑎 over 𝑏 to the 𝑛th power is equal to 𝑎 to
the 𝑛th power divided by 𝑏 to the 𝑛th power, our expression simplifies to two 𝑥
cubed over five cubed.
Next, we recall that to multiply
monomials, we multiply the coefficients and add the powers of the shared
variables. This means that two 𝑥 multiplied
by two 𝑥 multiplied by two 𝑥 is equal to eight 𝑥 cubed. And since five cubed is 125, our
expression simplifies to eight 𝑥 cubed over 125. This is an expression for the
volume of a cube whose side lengths are two 𝑥 over five.
