Question

Which expression is equivalent to 3√343x⁹y¹²z⁶?

A. 7x³y⁴z³
B. 7x³y⁶z²
C. 49x³y⁶z²
D. 49x³y⁴z²

Answer 1

The expression equivalent to
`\(3\sqrt[3]{343x^9y^(12)z^6}\)` is option B:
`\(7x^3y^6z^2\)`.

Step-by-step explanation:

The given expression
`\(3\sqrt[3]{343x^9y^(12)z^6}\)` can be simplified by expressin (343) as
`\(7^3\)`. This gives us
`\(3 * \sqrt[3]{7^3 \cdot x^9 \cdot y^(12) \cdot z^6}\)`.

Now, applying the properties of radicals, we can separate the cube root into three separate cube roots for each factor inside. This results in
`\(3 * \sqrt[3]{7^3} * \sqrt[3]{x^9} * \sqrt[3]{y^(12)} * \sqrt[3]{z^6}\)`.

Simplifying further, we get
`\(3 * 7 * x^3 * y^4 * z^2\)`, which can be written as
`\(21x^3y^4z^2\)`.

Comparing this with the given options, we find that option B
`\(7x^3y^6z^2\)` is the correct equivalent expression.

In conclusion, option B is the correct choice as it simplifies the given expression to its equivalent form, meeting the mathematical requirements outlined in the problem.