select all the expressions that are equivalent to $3^{3}cdot4^{3}$. $\frac{12^{7}}{12^{4}}$ $12^{6}$…
select all the expressions that are equivalent to $3^{3}cdot4^{3}$. $\frac{12^{7}}{12^{4}}$ $12^{6}$ $12^{9}$ $(12^{1})^{3}$
Answer
Explanation:
Step1: Calculate $3^{3}\cdot4^{3}$
According to the rule $(a\cdot b)^n=a^n\cdot b^n$, we have $3^{3}\cdot4^{3}=(3\times4)^{3}=12^{3}$.
Step2: Analyze $\frac{12^{7}}{12^{4}}$
According to the rule $\frac{a^{m}}{a^{n}}=a^{m - n}$, $\frac{12^{7}}{12^{4}}=12^{7 - 4}=12^{3}$.
Step3: Analyze $12^{6}$
$12^{6}\neq12^{3}$.
Step4: Analyze $12^{9}$
$12^{9}\neq12^{3}$.
Step5: Analyze $(12^{1})^{3}$
According to the rule $(a^{m})^{n}=a^{mn}$, $(12^{1})^{3}=12^{1\times3}=12^{3}$.
Answer:
$\frac{12^{7}}{12^{4}}$, $(12^{1})^{3}$