Sure, let's break down the problem step by step.
We are given the expression [tex]\(\sqrt[3]{0.3 \times 0.3 \times 0.3 \times 11 \times 11 \times 11}\)[/tex].
### Step 1: Simplify the Expression Inside the Cube Root
First, let's rewrite the expression in a clearer form. The expression inside the cube root is [tex]\(0.3^3 \times 11^3\)[/tex]. This is because multiplying 0.3 by itself three times gives [tex]\(0.3^3\)[/tex], and multiplying 11 by itself three times gives [tex]\(11^3\)[/tex].
So, we have:
[tex]\[ \sqrt[3]{0.3^3 \times 11^3} \][/tex]
### Step 2: Use the Property of Cube Roots
We can use the property of cube roots that [tex]\(\sqrt[3]{a \times b} = \sqrt[3]{a} \times \sqrt[3]{b}\)[/tex]. Applying this property, we get:
[tex]\[ \sqrt[3]{0.3^3 \times 11^3} = \sqrt[3]{0.3^3} \times \sqrt[3]{11^3} \][/tex]
### Step 3: Simplify Each Cube Root
Now, taking the cube root of each term individually:
[tex]\[ \sqrt[3]{0.3^3} = 0.3 \][/tex]
[tex]\[ \sqrt[3]{11^3} = 11 \][/tex]
### Step 4: Multiply the Results
Finally, we multiply the results of the simplified cube roots:
[tex]\[ 0.3 \times 11 = 3.3 \][/tex]
So, the value of [tex]\(\sqrt[3]{0.3 \times 0.3 \times 0.3 \times 11 \times 11 \times 11}\)[/tex] is [tex]\(\boxed{3.3}\)[/tex].
