Respuesta :
What is asked in the problem is the cube root of the given expression which is a product of the cube root of the numerical coefficient, 216, and that of the the variable, x^27. The cube root of 216 is 6 and that of x^27 is x^9. Thus, the answer is 6x^9.
The expression is [tex]\boxed{6{x^9}}[/tex] which is equivalent to [tex]\sqrt[3]{{216{x^{27}}}}[/tex] a perfect cube.Option (b) is correct.
Further Explanation:
Given:
The expression is [tex]\sqrt[3]{{216{x^{27}}}}.[/tex]
The options are as follows,
(a). [tex]6{x^3}[/tex]
(b). [tex]6{x^9}[/tex]
(c). [tex]72{x^3}[/tex]
(d). [tex]72{x^9}[/tex]
Calculation:
The given expression is [tex]\sqrt[3]{{216{x^{27}}}}.[/tex]
Consider the given expression as [tex]A = \sqrt[3]{{216{x^{27}}}}.[/tex]
Solve the above expression to obtain the simplest form.
[tex]\begin{aligned}A&= \sqrt[3]{{216{x^{27}}}}\\&= \sqrt[3]{{{{\left( 6 \right)}^3}{{\left( {{x^9}} \right)}^3}}}\\&=\sqrt[3]{{{{\left( {6{x^9}} \right)}^3}}}\\&= 6{x^9}\\\end{aligned}[/tex]
The simplest form of the expression is [tex]6{x^9}.[/tex]
The expression is [tex]\boxed{6{x^9}}[/tex] which is equivalent to [tex]\sqrt[3]{{216{x^{27}}}}[/tex] a perfect cube.Option (b) is correct.
Option (a) is not correct as the [tex]\sqrt[3]{{216{x^{27}}}}[/tex] is [tex]6{x^9}.[/tex]
Option (b) is correct as the [tex]\sqrt[3]{{216{x^{27}}}}[/tex] is [tex]6{x^9}.[/tex]
Option (c) is not correct as the [tex]\sqrt[3]{{216{x^{27}}}}[/tex] is [tex]6{x^9}.[/tex]
Option (d) is not correct as the [tex]\sqrt[3]{{216{x^{27}}}}[/tex] is [tex]6{x^9}.[/tex]
Learn more:
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Exponents and Powers
Keywords: Solution, perfect cube, factorized form, expression, difference of cubes, exponents, power, equation, power rule, exponent rule, 3 square root, [tex]216x^27[/tex], equivalent.
