Given:
[tex]\frac{21^x}{3^x}[/tex]
Aim:
We need to find the equivalent expression for the given expression.
Explanation:
[tex]Use\text{ }\frac{a^n}{b^n}=(\frac{a}{b})^n.\text{ Here a=21, b=3 and n=x.}[/tex]
[tex]\frac{21^x}{3^x}=(\frac{21}{3})^x[/tex][tex]Use\text{ 21=7}\times3\text{ in the given expression.}[/tex]
[tex]\frac{21^x}{3^x}=\frac{(7\times3)^x}{3^x}[/tex][tex]Use\text{ }(a\times b)^x=a^x\times b^x.\text{ Here a=7, b=3 and n=x.}[/tex]
[tex]\frac{21^x}{3^x}=\frac{7^x\times3^x}{3^x}[/tex]
Cancel out common terms.
[tex]\frac{21^x}{3^x}=7^x[/tex]
Final answer:
[tex]B.\frac{7^x\times3^x}{3^x}[/tex]
[tex]C.\text{ }7^x[/tex]
[tex]D.\text{ }(\frac{21}{3})^x[/tex]
