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{{ printedBook.courseTrack.name }} {{ printedBook.name }} A **perfect cube** is a number that can be written as the product of three identical integers. In other words, a number is a perfect cube if it is the cube of an integer.

Example | Rewrite as a Product | Perfect Cube? | Explanation |
---|---|---|---|

$125$ | $5×5×5=5_{3}$ | Yes | $5$ is an integer |

$166.375$ | $5.5×5.5×5.5=5.5_{3}$ | No | $5.5$ is not an integer |

Similarly, if a variable has an exponent that is a multiple of $3,$ it is said that it is a perfect cube. This is because this condition guarantees that the variable can be rewritten as the product of three identical powers with integer exponents. $y_{3}x_{6} ⇔y×y×y⇔x_{2}×x_{2}×x_{2} $