Question

Simplify:7^x+2-9.7^x/20*7^x​

Answer 1

Given:

The expression is:

$\dfrac{7^{x+2}-9\cdot 7^x}{-20\times 7^x}$

To find:

The simplified form of the given expression.

Solution:

We have,

$\dfrac{7^{x+2}-9\cdot 7^x}{-20\times 7^x}$

It can be written as

$\dfrac{7^{x+2}-9\cdot 7^x}{-20\times 7^x}=\dfrac{7^{x}\cdot 7^{2}-9\cdot 7^x}{-20\times 7^x}$

$\dfrac{7^{x+2}-9\cdot 7^x}{-20\times 7^x}=\dfrac{7^{x}(49-9)}{-20\times 7^x}$

Cancel out the common factors.

$\dfrac{7^{x+2}-9\cdot 7^x}{-20\times 7^x}=\dfrac{40}{-20}$

$\dfrac{7^{x+2}-9\cdot 7^x}{-20\times 7^x}=-2$

Therefore, the simplified value of the given expression is -2.