Answer:
Option 1
[tex]\sqrt[3]{216x^3y^6z^{12}}=6xy^2z^4[/tex]
Step-by-step explanation:
Given : Expression [tex]\sqrt[3]{216x^3y^6z^{12}}[/tex]
To find : Which expression is equivalent to given expression?
Solution :
The given expression is
[tex]\sqrt[3]{216x^3y^6z^{12}}[/tex]
We can write it as,
[tex]=(216x^3y^6z^{12})^{\frac{1}{3}}[/tex]
Applying power rule, [tex](x^a)^b=x^{a\times b}[/tex]
[tex]=(216)^\frac{1}{3}(x^3)^\frac{1}{3}(y^6)^\frac{1}{3}(z^{12})^{\frac{1}{3}}[/tex]
[tex]=(6^3)^\frac{1}{3}(x^3)^\frac{1}{3}(y^6)^\frac{1}{3}(z^{12})^{\frac{1}{3}}[/tex]
[tex]=6xy^2z^4[/tex]
Therefore, Option 1 is correct.
[tex]\sqrt[3]{216x^3y^6z^{12}}=6xy^2z^4[/tex]
