Question Video: Evaluating the Cube of a Number Mathematics

Which of the following is equal to (−10)³? [A] −100 [B] −1,000 [C] 1,000 [D] 1/1,000 [E] −1/1,000


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.

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