The expression is \(\boxed{6{x^9}}\) which is equivalent to \(\sqrt[3]{{216{x^{27}}}}\) a perfect cube.Option (b) is correct.
Further Explanation:
Given:
The expression is \(\sqrt[3]{{216{x^{27}}}}.\)
The options are as follows,
(a). \(6{x^3}\)
(b). \(6{x^9}\)
(c). \(72{x^3}\)
(d). \(72{x^9}\)
Calculation:
The given expression is \(\sqrt[3]{{216{x^{27}}}}.\)
Consider the given expression as \(A = \sqrt[3]{{216{x^{27}}}}.\)
Solve the above expression to obtain the simplest form.
\(\begin{aligned}A&= \sqrt[3]{{216{x^{27}}}}\\&= \sqrt[3]{{{{\left( 6 \right)}^3}{{\left( {{x^9}} \right)}^3}}}\\&=\sqrt[3]{{{{\left( {6{x^9}} \right)}^3}}}\\&= 6{x^9}\\\end{aligned}\)
The simplest form of the expression is \(6{x^9}.\)
The expression is \(\boxed{6{x^9}}\) which is equivalent to \(\sqrt[3]{{216{x^{27}}}}\) a perfect cube.Option (b) is correct.
Option (a) is not correct as the \(\sqrt[3]{{216{x^{27}}}}\) is \(6{x^9}.\)
Option (b) is correct as the \(\sqrt[3]{{216{x^{27}}}}\) is \(6{x^9}.\)
Option (c) is not correct as the \(\sqrt[3]{{216{x^{27}}}}\) is \(6{x^9}.\)
Option (d) is not correct as the \(\sqrt[3]{{216{x^{27}}}}\) is \(6{x^9}.\)
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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, \(216x^27\), equivalent.
