Answer :
To find the cube root of the expression
[tex]$$
8x^{27},
$$[/tex]
we can use the property that the cube root of a product is equal to the product of the cube roots. That is,
[tex]$$
\sqrt[3]{ab} = \sqrt[3]{a} \cdot \sqrt[3]{b}.
$$[/tex]
1. First, separate the given expression into two parts:
[tex]$$
\sqrt[3]{8x^{27}} = \sqrt[3]{8} \cdot \sqrt[3]{x^{27}}.
$$[/tex]
2. Compute the cube root of the numerical part:
[tex]$$
\sqrt[3]{8} = 2 \quad \text{since} \quad 2^3 = 8.
$$[/tex]
3. Next, compute the cube root of the variable part by using the rule of exponents for radicals:
[tex]$$
\sqrt[3]{x^{27}} = x^{27/3} = x^9.
$$[/tex]
4. Combine the two results to obtain the final answer:
[tex]$$
\sqrt[3]{8x^{27}} = 2 \cdot x^9 = 2x^9.
$$[/tex]
Thus, the cube root of [tex]$8x^{27}$[/tex] is
[tex]$$
\boxed{2x^9}.
$$[/tex]
[tex]$$
8x^{27},
$$[/tex]
we can use the property that the cube root of a product is equal to the product of the cube roots. That is,
[tex]$$
\sqrt[3]{ab} = \sqrt[3]{a} \cdot \sqrt[3]{b}.
$$[/tex]
1. First, separate the given expression into two parts:
[tex]$$
\sqrt[3]{8x^{27}} = \sqrt[3]{8} \cdot \sqrt[3]{x^{27}}.
$$[/tex]
2. Compute the cube root of the numerical part:
[tex]$$
\sqrt[3]{8} = 2 \quad \text{since} \quad 2^3 = 8.
$$[/tex]
3. Next, compute the cube root of the variable part by using the rule of exponents for radicals:
[tex]$$
\sqrt[3]{x^{27}} = x^{27/3} = x^9.
$$[/tex]
4. Combine the two results to obtain the final answer:
[tex]$$
\sqrt[3]{8x^{27}} = 2 \cdot x^9 = 2x^9.
$$[/tex]
Thus, the cube root of [tex]$8x^{27}$[/tex] is
[tex]$$
\boxed{2x^9}.
$$[/tex]
