College

What is the cube root of [tex]$27x^{18}$[/tex]?

A. [tex]$3x^6$[/tex]
B. [tex]$3x^9$[/tex]
C. [tex]$9x^6$[/tex]
D. [tex]$9x^9$[/tex]

Answer :

To find the cube root of

[tex]$$27x^{18},$$[/tex]

we can simplify the expression step by step.

1. Notice that

[tex]$$27 = 3^3.$$[/tex]

The cube root of [tex]$3^3$[/tex] is [tex]$3$[/tex].

2. For the variable part, we have

[tex]$$x^{18}.$$[/tex]

Taking the cube root gives

[tex]$$\sqrt[3]{x^{18}} = x^{\frac{18}{3}} = x^6.$$[/tex]

3. Combining these results:

[tex]$$\sqrt[3]{27x^{18}} = \sqrt[3]{27} \cdot \sqrt[3]{x^{18}} = 3 \cdot x^6 = 3x^6.$$[/tex]

Thus, the correct answer is

[tex]$$\boxed{3x^6}.$$[/tex]