Given x, is greater than, 0x>0 and y, is greater than, 0, commay>0, select the expression that is equivalent tocube root of, 216, x, to the power 9 , y, squared, end cube root3 216x 9 y 2
Question
Given x, is greater than, 0x>0 and y, is greater than, 0, commay>0, select the expression that is equivalent tocube root of, 216, x, to the power 9 , y, squared, end cube root3 216x 9 y 2
Solution
The expression equivalent to the cube root of 216x^9y^2 is 6x^3y^(2/3).
Here's the step-by-step solution:
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The cube root of a number is the same as raising that number to the power of 1/3. So, we can rewrite the expression as (216x^9y^2)^(1/3).
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When you raise a power to a power, you multiply the exponents. So, we can rewrite the expression as 216^(1/3) * (x^9)^(1/3) * (y^2)^(1/3).
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The cube root of 216 is 6, so 216^(1/3) simplifies to 6.
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(x^9)^(1/3) simplifies to x^(9*1/3) = x^3.
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(y^2)^(1/3) simplifies to y^(2*1/3) = y^(2/3).
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Therefore, the expression simplifies to 6x^3y^(2/3).
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