Question

14 power n+4 +7 power n+3* 2 power n+3 upon 13*14 n +14 n

Answer 1

QUESTION:

Find the value of $\frac{14^{n+4} +(7^{n+3} \times 2^{n+3})}{(13 \times 14^n) +14^n} .$

ANSWER:

The value of the given expression $\frac{14^{n+4} +(7^{n+3} \times 2^{n+3})}{(13 \times 14^n) +14^n}$ will be 2940.

Given,

Expression:

$\frac{14^{n+4} +(7^{n+3} \times 2^{n+3})}{(13 \times 14^n) +14^n} .$

To find,

Value of the given expression.

Solution,

We can see that the given expression here, is

$\frac{14^{n+4} +(7^{n+3} \times 2^{n+3})}{(13 \times 14^n) +14^n} .$

To find the value of the above expression, we need to use some of the rules of exponents, which are as follows.

• $a^{m+n}=a^ma^n$

• $a^m \times b^m=(a\times b)^m$

So, we can express the given expression as

$\frac{14^{n+4} +(7^{n+3} \times 2^{n+3})}{(13 \times 14^n) +14^n} =\frac{14^n \times 14^4+(14^{n+3})}{14^n \times (13+1)}$

$\implies \frac{14^{n+4} +(7^{n+3} \times 2^{n+3})}{(13 \times 14^n) +14^n} =\frac{14^n \times 14^4+14^n\times 14^3}{14^n \times 14}$

$\implies \frac{14^{n+4} +(7^{n+3} \times 2^{n+3})}{(13 \times 14^n) +14^n} =\frac{14^n \times 14^3(14+1)}{14^n \times 14}$

$\implies \frac{14^{n+4} +(7^{n+3} \times 2^{n+3})}{(13 \times 14^n) +14^n} =14^2(15) = 196 \times 15$

$\implies \frac{14^{n+4} +(7^{n+3} \times 2^{n+3})}{(13 \times 14^n) +14^n} =2940.$

Therefore, the value of the given expression $\frac{14^{n+4} +(7^{n+3} \times 2^{n+3})}{(13 \times 14^n) +14^n}$ will be 2940.

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