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