Answer :
To find the cube root of the expression
$$8x^{27},$$
we start by recognizing that the cube root of a product can be written as the product of the cube roots. That is,
$$\sqrt[3]{8x^{27}} = \sqrt[3]{8} \cdot \sqrt[3]{x^{27}}.$$
1. For the numeric part:
$$\sqrt[3]{8} = 2,$$
because $2^3 = 8$.
2. For the variable part:
$$\sqrt[3]{x^{27}} = x^{27/3} = x^9,$$
since the cube root of a power is the same as dividing the exponent by 3.
Multiplying these results together gives:
$$\sqrt[3]{8x^{27}} = 2 \cdot x^9 = 2x^9.$$
Therefore, the correct answer is
$$\boxed{2 x^9}.$$
$$8x^{27},$$
we start by recognizing that the cube root of a product can be written as the product of the cube roots. That is,
$$\sqrt[3]{8x^{27}} = \sqrt[3]{8} \cdot \sqrt[3]{x^{27}}.$$
1. For the numeric part:
$$\sqrt[3]{8} = 2,$$
because $2^3 = 8$.
2. For the variable part:
$$\sqrt[3]{x^{27}} = x^{27/3} = x^9,$$
since the cube root of a power is the same as dividing the exponent by 3.
Multiplying these results together gives:
$$\sqrt[3]{8x^{27}} = 2 \cdot x^9 = 2x^9.$$
Therefore, the correct answer is
$$\boxed{2 x^9}.$$
