Question

Обьясните как решать: 196 в степени n+1 разделить 2 в степени 2n+1 умножить на 7 в степени 2n

Answer 1

условие можно понять двояко
выберите сами правильное условие и соответствующее решение

196^( n+1) / 2 ^(2n+1) * 7^2n = (2^2*7^2)^( n+1)/ 2 ^(2n+1) * 7^2n =
=2^(2*( n+1)-(2n+1)) * 7^(2*( n+1)+2n) = 2^1 * 7^(4*n+1) =2 * 7^(4*n+1)

196^( n+1) / {2 ^(2n+1) * 7^2n} = (2^2*7^2)^( n+1)/ 2 ^(2n+1) * 7^(-2n) =
=2^(2*( n+1)-(2n+1)) * 7^(2*( n+1)-2n) = 2^1 * 7^1=14

Answer 2

196^(n+1) / (2^(2n+1) *7 ^(2n))=196* 196^n / (2*2^(2n)*7^(2n))= 196*(14^2)^n / (2* (2*7)^(2n))= 196*(14)^(2n)/ (2*14^(2n))=196/2=98                 

Answer 3

Solving the Expression 196^(n+1) / 2^(2n+1) * 7^(2n)

To solve the expression 196^(n+1) / 2^(2n+1) * 7^(2n), we can break it down step by step.

Step 1: Simplify the Expression

First, let's simplify the expression by breaking down each term and applying the rules of exponents.

Step 2: Simplify 196^(n+1)

196 can be expressed as 14^2. Therefore, 196^(n+1) can be simplified to (14^2)^(n+1), which equals 14^(2n+2).

Step 3: Simplify 2^(2n+1)

2^(2n+1) can be expanded to (2^2)^n * 2, which equals 4^n * 2.

Step 4: Simplify 7^(2n)

7^(2n) remains as 7^(2n).

Step 5: Combine the Simplified Terms

Now, we can combine the simplified terms to get the final expression: 14^(2n+2) / (4^n * 2) * 7^(2n).

Step 6: Further Simplification

We can simplify this expression further by using the properties of exponents and division.

Step 7: Final Simplified Expression

The final simplified expression is: (14^(2n+2) * 7^(2n)) / (4^n * 2).

This is the simplified form of the given expression.

I hope this helps! If you have any further questions or need additional assistance, feel free to ask.