Which expression is equivalent to 3√(216x^27)? 6x^3 6x^9 72x^3 72x^9
The Correct Answer and Explanation is:
We are given the expression: 3216×2733\sqrt[3]{216x^{27}}
Step 1: Simplify the cube root
We want to simplify the cube root of the expression inside the radical: 216×273\sqrt[3]{216x^{27}}
First, break this into two parts: 2163⋅x273\sqrt[3]{216} \cdot \sqrt[3]{x^{27}}
- The cube root of 216 is:
2163=6(since 63=216)\sqrt[3]{216} = 6 \quad \text{(since } 6^3 = 216\text{)}
- The cube root of x²⁷ is:
x273=x27/3=x9\sqrt[3]{x^{27}} = x^{27/3} = x^9
So we now have: 216×273=6×9\sqrt[3]{216x^{27}} = 6x^9
Step 2: Multiply by the 3 outside the radical
Now multiply this result by the 3 that was outside the cube root: 3⋅(6×9)=18×93 \cdot (6x^9) = 18x^9
Step 3: Check the answer choices
We are given four options:
- A) 6x36x^3
- B) 6x96x^9
- C) 72x372x^3
- D) 72x972x^9
But none of these options say 18x⁹, which is the correct simplification.
Let’s double-check the problem. The original problem might have a typo — perhaps it meant: 3⋅8×273(instead of 216)?3 \cdot \sqrt[3]{8x^{27}} \quad \text{(instead of 216)?}
However, based on the input exactly as you typed it: 3216×273=3⋅6×9=18×93\sqrt[3]{216x^{27}} = 3 \cdot 6x^9 = 18x^9
So the correct equivalent expression is: 18×9\boxed{18x^9}
Since 18x⁹ is not one of the listed options, the correct answer is not among the choices. If this was a multiple-choice question, the options may contain a mistake. Please double-check the original question.
