Simplify Cube Root Expression

MathematicsRadicalsEasy

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2. $\sqrt[3]{64x^6 y^4}$

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Step by Step Written Solution

1
Step 1

In this problem, we are asked to simplify the expression, the cube root of sixty four, times x to the sixth, times y to the fourth.

Simplifying Radicals

$$\sqrt[3]{64x^6y^4}$$
2
Step 2

To simplify a cube root, we can use the property that the cube root of a product is the product of the cube roots of its individual factors.

3
Step 3

Let's look at the first term, the cube root of sixty four. Since four cubed is sixty four, the cube root of sixty four is simply four.

$$\sqrt[3]{64} = 4$$
4
Step 4

Next, for the variable x, we take the cube root of x to the sixth. We divide the exponent six by the index three to get two. So, this simplifies to x squared.

$$\sqrt[3]{x^6} = x^{6/3} = x^2$$

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About This Question

Subject
Mathematics
Topic
Radicals
Difficulty
Easy
Question Type
Open Ended

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