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Simplify the square root of the cube root of 64π₯ to the 72nd.
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We need to work from the inside out.
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So first, we need to evaluate the cube root.
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So do we know the cube root of 64?
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64 is four times four times four.
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So the cube root of 64 is four.
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So in writing our answer, letβs not forget the big square root.
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So the cube root of 64 we know is four.
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So now the cube root of π₯ to the 72nd.
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Now, when finding the cube root of π₯ to the 72nd power, we have to be careful.
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Itβs a little different than taking the cube root of 64.
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When we take the cube root of 64, we need to find a number when multiplied to itself three times we get 64.
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And that is four times four times four.
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Now, the same thing is true with π₯ to the 72nd, except when multiplying, we add our exponents.
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So what number can we add to itself three times that gives us 72?
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That would be 24.
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So the cube root of π₯ to the 72nd is π₯ to the 24th.
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So now we need to take the square root of four π₯ to the 24th.
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Now, the square root of four is two.
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Itβs two times two.
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Now again, π₯ to the 24th, what number when added to itself gives us 24?
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That would be π₯ to the 12th because 12 plus 12 is 24.
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Therefore, our final answer is two π₯ to the 12th power.