Question

Which expression is equivalent to 3 square root 216x^27? 6x3 6x9 72x3 72x9

Answer 1

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 $6{x^9}.$

Learn more:

1. Learn more about unit conversion brainly.com/question/4837736
2. Learn more about non-collinear brainly.com/question/4165000
3. 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, $216x^27$, equivalent.

Answer 2

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.