Question

Simplify (5^x+2-5^x)/5^x×4

Answer 1

6

Explanation:

The given expression is,

`(5^(x+2)-5^x )/(5^x*4)`

Now, we know that,

`a^(m+n) = a^m . a^n`

Then,

`5^(x+2)=5^x . 5^2`

So,

`(5^(x+2)-5^x)/(5^x*4)=(5^x.5^2-5^x)/(5^x*4)`

Now, taking
`5^(x)` common from the numerator of the given expression, then

`(5^(x+2)-5^x)/(5^x*4)=(5^x(5^2-1))/(5^x*4)`

`\implies(5^(x+2)-5^x )/(5^x*4)=(5^2-1)/(4)`

`\implies(5^(x+2)-5^x)/(5^x*4)=(5*5-1)/(4)=(25-1)/(4)`

`\implies(5^(x+2)-5^x)/(5^x*4)=(24)/(4)=6`

So, the simplified form of the given expression gives the result 6.