which expression is equivalent to $sqrt3{343x^{9}y^{12}z^{6}}$?\n$7x^{3}y^{4}z^{2}$\n$7x^{3}y^{6}z^{2}$\n$49x…
which expression is equivalent to $sqrt3{343x^{9}y^{12}z^{6}}$?\n$7x^{3}y^{4}z^{2}$\n$7x^{3}y^{6}z^{2}$\n$49x^{3}y^{6}z^{2}$\n$49x^{3}y^{4}z^{2}$
Answer
Explanation:
Step1: Find cube - root of coefficient
Find $\sqrt[3]{343}$. Since $7\times7\times7 = 343$, $\sqrt[3]{343}=7$.
Step2: Apply exponent rule for variables
For $x^{9}$, using the rule $\sqrt[n]{a^{m}}=a^{\frac{m}{n}}$, when $n = 3$ and $m = 9$, we have $x^{\frac{9}{3}}=x^{3}$.
Step3: Apply exponent rule for $y$
For $y^{12}$, with $n = 3$ and $m = 12$, $y^{\frac{12}{3}}=y^{4}$.
Step4: Apply exponent rule for $z$
For $z^{6}$, with $n = 3$ and $m = 6$, $z^{\frac{6}{3}}=z^{2}$.
Step5: Combine results
The equivalent expression is $7x^{3}y^{4}z^{2}$.
Answer:
A. $7x^{3}y^{4}z^{2}$