\[\left(x^4\cdot y^4\right)^{3}=?\]
Choose 1 answer:
Choose 1 answer:
(Choice A)
\[x^{24}\cdot y^{24}\]
A
\[x^{24}\cdot y^{24}\]
(Choice B)
\[x^{12}\cdot y^{12}\]
B
\[x^{12}\cdot y^{12}\]
(Choice C)
\[x^{7}\cdot y^{7}\]
C
\[x^{7}\cdot y^{7}\]
(Choice D)
\[x^{64}\cdot y^{64}\]
D
\[x^{64}\cdot y^{64}\]
To simplify the expression $\left(x^4\cdot y^4\right)^{3}$, we need to raise both $x^4$ and $y^4$ to the power of $3$. When we raise a power to another power, we multiply the exponents. Therefore, we have:
$\left(x^4\right)^3 \cdot \left(y^4\right)^3 = x^{4\cdot 3} \cdot y^{4\cdot 3} = x^{12} \cdot y^{12}$
So, the simplified expression is $x^{12} \cdot y^{12}$. Therefore, the answer is $\boxed{\text{(B)}}\ x^{12}\cdot y^{12}$.