The equivalent expressions [tex]$\frac{21^x}{7^x}[/tex] is [tex]$3^{x}$[/tex].
What is an equivalent expression?
Equivalent expressions exist as expressions that work exactly even though they look different. If two algebraic expressions exist as equivalent, then the two expressions contain the exact value when we plug in the same values for the variables.
Given: [tex]$\frac{21^x}{7^x}[/tex]
Factor [tex]$21^{x} = 7^{x} \cdot 3^{x}$[/tex]
[tex]$=\frac{7^{x} \cdot 3^{x}}{7^{x}}$[/tex]
Cancel the common factor: [tex]$7^{x}$[/tex]
[tex]$=3^{x}$[/tex]
Therefore, the correct answer is option B. [tex]$3^{x}$[/tex].
To learn more about equivalent expressions
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