Question

Simplify:- 15×5^n+1 + 20 × 5^n × 5 / 3 × 5^n+2 + 20×5^n+1 ​

Answer 1

Answer:

You need to eliminate the annoying exponent factor. And it is easy to convert all such factors to 5^(n+1).

Numerator =10.5^(n+1)+5.5.5^(n) =10.5^(n+1)+5.5^(n+1) =15.5^(n+1)

Denominator =3.5.5^(n+1)+10.5^(n+1) = 15.5^(n+1)+10.5^(n+1) =25.5^(n+1)

Now in the given question the factor 5^(n+1) is removed from numerator and denominator, thus it reduces to 15/25 =3/5.

Answer 2

Answer:

1

Step-by-step explanation:

$15*5^{n+ 1} +20*5^{n}*5/3*5^{n+ 2} +20*5^{n+1}\\5*5^{n+ 1} +20*5^{n}*5/5^{n+ 2} +20*5^{n+1}\\5^{n+ 1} +20*5^{n}*5/5^{n+ 2} +4*5^{n+1}\\5^{n+ 1} +20*5^{n}*5/5^{n+ 2} +4*5^{n+1}\\20*5^{n}*5/5^{n+ 2} +4\\5*5^{n}*5/5^{n+ 2} \\5^{n}*5*5/5^{n+ 2} \\5^{n+2} = 5^{n} *5*5\\1$

Hope it will help you