### Video Transcript

Which of the following is equal to
negative 10 cubed? Is it (A) negative 100, (B)
negative 1,000, (C) 1,000, (D) one one thousandth, or (E) negative one one
thousandth.

We begin by recalling that raising
a number to the power of three is the same as cubing that number. When cubing any number, we multiply
it by itself and itself again. This means that to calculate
negative 10 cubed, we need to multiply negative 10 by negative 10 by negative
10. When multiplying two positive
numbers or two negative numbers, we get a positive answer. However, when we multiply a
negative by a positive or positive by a negative, we get a negative answer.

In this question, we begin by
multiplying negative 10 by negative 10. As there are two negatives, our
answer will be positive, and 10 multiplied by 10 is 100. We now need to multiply 100 by
negative 10. We’re multiplying a positive number
by a negative number. This will give us a negative
answer. And as 100 multiplied by 10 is
1,000, 100 multiplied by negative 10 is negative 1,000. This means that the correct answer
is option (B). Negative 1,000 is equal to negative
10 cubed.

Before answering one final
question, we will look at how we can cube integers to help us calculate the volume
of shapes. We know that the volume of any
three-dimensional shape is the space inside it, and it is measured in cubic units,
for example, cubic centimeters or cubic meters. A cube is a three-dimensional
shape, where the length of each vertex or side is the same. If we let the length of each vertex
or side be 𝑠 units, then the volume of the cube will be equal to the length
multiplied by the width multiplied by the height, in other words, 𝑠 multiplied by
𝑠 multiplied by 𝑠. Using our knowledge of cube
numbers, we know that we can write this as 𝑠 cubed. The volume of any cube is equal to
the side length cubed.