Question

Simplify (5^x+2-5^x)/5^x×4

Answer 1

Answer:

6

Step-by-step explanation:

The given expression is,

$\frac{5^{x+2}-5^x }{5^x\times4}$

Now, we know that,

$a^{m+n} = a^m . a^n$

Then,

$5^{x+2}=5^x . 5^2$

So,

$\frac{5^{x+2}-5^x}{5^x\times4}=\frac{5^x.5^2-5^x}{5^x\times4}$

Now, taking $5^{x}$ common from the numerator of the given expression, then

$\frac{5^{x+2}-5^x}{5^x\times4}=\frac{5^x(5^2-1)}{5^x\times4}$

$\implies\frac{5^{x+2}-5^x }{5^x\times4}=\frac{5^2-1}{4}$

$\implies\frac{5^{x+2}-5^x}{5^x\times4}=\frac{5\times5-1}{4}=\frac{25-1}{4}$

$\implies\frac{5^{x+2}-5^x}{5^x\times4}=\frac{24}{4}=6$

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