The expression is
which is equivalent to
a perfect cube.Option (b) is correct.
Further Explanation:
Given:
The expression is ![\sqrt[3]{{216{x^{27}}}}.](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%7B216%7Bx%5E%7B27%7D%7D%7D%7D.)
The options are as follows,
(a). ![6{x^3}](https://tex.z-dn.net/?f=6%7Bx%5E3%7D)
(b). ![6{x^9}](https://tex.z-dn.net/?f=6%7Bx%5E9%7D)
(c). ![72{x^3}](https://tex.z-dn.net/?f=72%7Bx%5E3%7D)
(d). ![72{x^9}](https://tex.z-dn.net/?f=72%7Bx%5E9%7D)
Calculation:
The given expression is ![\sqrt[3]{{216{x^{27}}}}.](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%7B216%7Bx%5E%7B27%7D%7D%7D%7D.)
Consider the given expression as ![A = \sqrt[3]{{216{x^{27}}}}.](https://tex.z-dn.net/?f=A%20%3D%20%5Csqrt%5B3%5D%7B%7B216%7Bx%5E%7B27%7D%7D%7D%7D.)
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}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DA%26%3D%20%5Csqrt%5B3%5D%7B%7B216%7Bx%5E%7B27%7D%7D%7D%7D%5C%5C%26%3D%20%5Csqrt%5B3%5D%7B%7B%7B%7B%5Cleft%28%206%20%5Cright%29%7D%5E3%7D%7B%7B%5Cleft%28%20%7B%7Bx%5E9%7D%7D%20%5Cright%29%7D%5E3%7D%7D%7D%5C%5C%26%3D%5Csqrt%5B3%5D%7B%7B%7B%7B%5Cleft%28%20%7B6%7Bx%5E9%7D%7D%20%5Cright%29%7D%5E3%7D%7D%7D%5C%5C%26%3D%206%7Bx%5E9%7D%5C%5C%5Cend%7Baligned%7D)
The simplest form of the expression is ![6{x^9}.](https://tex.z-dn.net/?f=6%7Bx%5E9%7D.)
The expression is
which is equivalent to
a perfect cube.Option (b) is correct.
Option (a) is not correct as the
is ![6{x^9}.](https://tex.z-dn.net/?f=6%7Bx%5E9%7D.)
Option (b) is correct as the
is ![6{x^9}.](https://tex.z-dn.net/?f=6%7Bx%5E9%7D.)
Option (c) is not correct as the
is ![6{x^9}.](https://tex.z-dn.net/?f=6%7Bx%5E9%7D.)
Option (d) is not correct as the
is ![6{x^9}.](https://tex.z-dn.net/?f=6%7Bx%5E9%7D.)
Learn more:
- Learn more about unit conversion brainly.com/question/4837736
- Learn more about non-collinear brainly.com/question/4165000
- Learn more aboutbinomial and trinomial brainly.com/question/1394854
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,
, equivalent.