Simplify the expression (2^n+4^n)/(6^n)

 Exercise

$\frac{\left(2^n+4^n\right)}{6^n}$

 

Expand the fraction $\frac{2^n+4^n}{6^n}$ into $2$ simpler fractions with common denominator $6^n$

$\frac{2^n}{6^n}+\frac{4^n}{6^n}$

 

Rewrite $\frac{2^n}{6^n}$ using the property of the power of a quotient: $\displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$

$\left(\frac{2}{6}\right)^n+\frac{4^n}{6^n}$

 

Rewrite $\frac{4^n}{6^n}$ using the property of the power of a quotient: $\displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$

$\left(\frac{2}{6}\right)^n+\left(\frac{4}{6}\right)^n$

 

Divide $2$ by $6$

$\left(\frac{1}{3}\right)^n+\left(\frac{4}{6}\right)^n$

 

Divide $4$ by $6$

$\left(\frac{1}{3}\right)^n+\left(\frac{2}{3}\right)^n$

$\left(\frac{1}{3}\right)^n+\left(\frac{2}{3}\right)^n$

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