simplify $$ \frac{3^{2 n}-9^{n+1}}{72^{n}} $$

Question

UpStudy AI · Accepted Answer

Calculate or simplify the expression $$ (3^(2*n)-9^(n+1))/72^n $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{\left(3^{2n}-9^{n+1}ight)}{72^{n}}$$
- step1: Remove the parentheses:
  $$\frac{3^{2n}-9^{n+1}}{72^{n}}$$
- step2: Subtract the terms:
  $$\frac{-8	imes 3^{2n}}{72^{n}}$$
- step3: Rewrite the fraction:
  $$-\frac{8	imes 3^{2n}}{72^{n}}$$
- step4: Factor the expression:
  $$-\frac{8	imes 3^{2n}}{8	imes 9	imes 72^{n-1}}$$
- step5: Reduce the fraction:
  $$-\frac{3^{2n}}{9	imes 72^{n-1}}$$
- step6: Factor the expression:
  $$-\frac{3^{2n}}{3^{2}	imes 72^{n-1}}$$
- step7: Divide the numbers:
  $$-\frac{3^{2n-2}}{72^{n-1}}$$
- step8: Factor the expression:
  $$-\frac{3^{2n-2}}{3^{2n-2}	imes 8^{n-1}}$$
- step9: Reduce the fraction:
  $$-\frac{1}{8^{n-1}}$$
The simplified form of the expression $$ \frac{3^{2n}-9^{n+1}}{72^n} $$ is $$ -\frac{1}{8^{n-1}} $$.
The simplified form is $$ -\frac{1}{8^{n-1}} $$.

simplify

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Algebra Questions