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The problem asks to solve the following equation:

\[
\frac{\sqrt[3]{0.512}}{x} = \sqrt[3]{1000000}
\]

We need to find the value of \( x \).

### Step 1: Simplify both cube roots
- \( \sqrt[3]{0.512} = 0.8 \) because \( 0.8^3 = 0.512 \)
- \( \sqrt[3]{1000000} = 100 \) because \( 100^3 = 1000000 \)

### Step 2: Substitute these values into the equation

\[
\frac{0.8}{x} = 100
\]

### Step 3: Solve for \( x \)

Multiply both sides by \( x \) to eliminate the denominator:

\[
0.8 = 100x
\]

Now, divide both sides by 100:

\[
x = \frac{0.8}{100} = 0.008
\]

Thus, the value of \( x \) is \( \boxed{0.008} \).

### Answer:
The correct option is \( a. 0.008 \).

Would you like further details on this solution or have any questions?

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Here are some related questions:
1. What is the cube root of 27?
2. How do you find the cube root of a number without a calculator?
3. If \( x = \sqrt[3]{64} \), what is the value of \( x \)?
4. What is the square root of 0.64?
5. How can cube roots be applied in geometry?

**Tip**: Cube roots are useful for determining volumes and scaling factors in 3D shapes!

Solve: Cube root of 0.512 divided by x equals the cube root of 1,000,000. Find the value of x.

Find the value of x in the equation where the cube root of 0.512 divided by x equals the cube root of 1,000,000. This step-by-step solution simplifies cube roots and uses basic algebra to solve for x. Perfect for students in grades 8-10.

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