Question

Answer pls
Very fast plzzzz

Answer 1

6^-5 x 6^2n+1=6^13÷6^7

6^2n-4=16^13/7

Now compairing powers,

2n-4=13/7

14n-28=13

14n=41

n=41/14

Answer 2

Question

$\sf 6^{-5}\times 6^{2n+1}=6^{13}\div 6^7$

Answer

Step 1: Find the value of RHS. Use this law to do so ⇒ $\sf a^{m}\div a^{n} =a^{m-n}$

⇒ $\sf 6^{-5}\times 6^{2n+1}=6^{13}\div 6^7$

⇒ $\sf 6^{-5}\times 6^{2n+1}=6^{13-7}$

⇒ $\sf 6^{-5}\times 6^{2n+1}=6^{6}$

$\rule{300}{0.5}$

Step 2: Since the base of all the numbers is '6' we will form an equation with all the exponents.

We have to use this law too ⇒ $\sf a^{m} \times a^{n}=a^{m+n}$

Our equation would be ⇒ $\sf -5+(2n+1) = 6$

Let's solve your equation step-by-step.

$\sf -5+(2n+1) = 6$

Step 1: Simplify both sides of the equation.

⇒ $\sf -5+2n+1 = 6$

(Combine Like Terms)

⇒ $\sf (2n)+(-5+1)=6$

⇒ $\sf 2n+-4=6$

⇒ $\sf 2n-4=6$

Step 2: Add 4 to both sides.

⇒ $\sf 2n-4+4=6+4$

⇒ $\sf 2n=10$

Step 3: Divide both sides by 2.

⇒ $\sf \frac{2n}{2}=\frac{10}{2}$

⇒ $\sf n= 5$

Verification if n = 5

⇒ $\sf -5+(2n+1) = 6$

⇒ $\sf -5+[(2\times 5) +1 ]= 6$

⇒ $\sf -5+[10 +1 ]= 6$

⇒ $\sf -5+11= 6$

⇒ $\sf 6=6$

$\rule{300}{0.5}$

∴ n = 5 in the equation ⇒  $\sf \bf 6^{-5}\times 6^{2n+1}=6^{13}\div 6^7$