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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]
[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]
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