ANSWER
A, B, and C
EXPLANATION
We want to find the expressions that are equivalent to the given expression:
[tex]\frac{21^x}{7^x}[/tex]
First, let us simplify the given expression using the following law of exponents:
[tex]\frac{a^c}{b^c}=(\frac{a}{b})^c[/tex]
Therefore, we have that the expression becomes:
[tex]\frac{21^x}{7^x}=(\frac{21}{7})^x=3^x[/tex]
Another way of simplifying the expression is to simplify the numerator using the following law of exponents:
[tex](a*b)^x=a^x*b^x[/tex]
Therefore, the expression becomes:
[tex]\begin{gathered} \frac{21^x}{7^x}=\frac{(7*3)^x}{7^x} \\ \\ \Rightarrow\frac{7^x*3^x}{7^x} \\ \\ \Rightarrow3^x \end{gathered}[/tex]
Therefore, we see that the expressions that are equivalent to the given one are:
[tex]\begin{gathered} 3^x \\ \\ \frac{7^x*3^x}{7^x} \\ \\ (\frac{21}{7})^x \end{gathered}[/tex]
The correct options are A, B, and C.
