which expression is equivalent to $(2x^{4}y)^{3}$?\n$2x^{7}y^{4}$\n$2x^{12}y^{3}$\n$8x^{7}y^{4}$\n$8x^{12}y^{…
which expression is equivalent to $(2x^{4}y)^{3}$?\n$2x^{7}y^{4}$\n$2x^{12}y^{3}$\n$8x^{7}y^{4}$\n$8x^{12}y^{3}$
Answer
Explanation:
Step1: Apply the power - of - a - product rule ((ab)^n=a^nb^n)
$$(2x^{4}y)^{3}=2^{3}(x^{4})^{3}y^{3}$$
Step2: Calculate (2^{3}) and apply the power - of - a - power rule ((a^{m})^{n}=a^{mn})
- Calculate (2^{3}): (2^{3}=8)
- For ((x^{4})^{3}), using ((a^{m})^{n}=a^{mn}), we have (x^{4\times3}=x^{12})
So, ((2x^{4}y)^{3}=8x^{12}y^{3})
Answer:
(8x^{12}y^{3}) (the fourth option)