Find the cube root of each of the following numbers by prime Factorization method:

– 27000

-27000

-27000 can be written as -27 × 1000.

Prime Factorization of 27:

⇒ 27 = 3 × 3 × 3

= 3³

Prime Factorization of 1000:

⇒ 1000 = (2 × 2 × 2) × (5 × 5 × 5)

= (2³ × 5³)

= 10³

⇒ = (-27 × 1000)^1/3

= (-3³ × 10³)^1/3

= (-30³)^1/3

We know that by laws of exponents, (a^m)ⁿ = a^mn.

We know that cube root of a negative number is negative.

∴ = -30