Question

Which monomials are perfect cubes? Check all that apply.

Answer 1

A perfect cube is a number that resulted from multiplying a number three times by itself. A perfect cube is also a number that has an exact cube root.

8x^12 ⇒ 2x^4 * 2x^4 * 2x^4
27x^9 ⇒ 3x³ * 3x³ * 3x³

Only two monomials are perfect cubes.

Answer 2

When a number is multiplied by itself three times, then the resultant number is called a perfect cube. It is also a number with an exact cube root.

Out of the given options, $8x^{12}$ and $27x^{9}$ are perfect cubes.

$8x^{12}$ = $2x^{4}\times 2x^{4}\times 2x^{4}$ (2's are multiplied and powers are added)

$27x^{9}$ = $3x^{3}\times 3x^{3}\times 3x^{3}$ (3's are multiplied and powers are added)