Question

Which expression is equivalent to

1/100c^3d^4
1/100c^6d^9
1/10c^3d^4
1/10c^6d^9

Answer 1

1/10c^3d^4

Explanation:

A cube root is an operation which splits expressions and numbers within it into 3 groups of the exact same size. These groups when multiplied by themselves make the expressions and numbers under the root. For example, ∛27 = 3 since 3*3*3 = 27.

Take each part under the cube root and split it into three equal groups.

1/ 1000 = 1/10 * 1/10 * 1/10 so ∛1/1000 = 1/10

c^9 = c^3*c^3*c^3 so ∛c^9 = c^3

d^12 = d^4*d^4*d^4 so ∛d^12 = d^4

Together ∛1/1000 c^9 d^12 = 1/10 * c^3 * d^4