Video Transcript
The volume of a cube is one-quarter
cubed of a cubic unit. Express this as a product,
evaluating the volume of the cube.
In this question, we are told that
the expression one-quarter cubed represents the volume of a cube, with the units of
cubic units. We need to rewrite this expression
as a product and then use this expression to evaluate the volume of the cube.
To do this, we can start by
recalling what is meant by the cube of a number. In general, if π is a positive
integer, then π to the power of π is the product of π lots of π. In our case, the value of π, which
is called the base, is one-quarter. And the value of the exponent π is
three. So one-quarter cubed is the product
of three lots of one-quarter, as shown.
We can then recall that we evaluate
the product of rational numbers by multiplying their numerators and
denominators. This gives us one times one times
one over four times four times four. We can then evaluate the products
in the numerator and denominator separately. We have one times one times one is
equal to one and four times four times four is equal to 64, giving us one over
64.
We are told to give our answer as a
product that we evaluate. And we know that this represents
the volume of a cube. So we should also include units in
the same way we are given in the question.
It is also worth noting that this
was not the only way we couldβve evaluated the volume of this cube. We can also recall that π over π
all raised to the power of π is equal to π to the πth power over π to the πth
power. This would give us that one-quarter
cubed is one cubed over four cubed, which we could evaluate to once again obtain one
over 64. In either case, we can see that the
volume of the cube can be expressed as one-quarter times one-quarter times
one-quarter, which is equal to one sixty-fourth of a cubic unit.
