Answer:
6
Step-by-step explanation:
The given expression is,
[tex]\frac{5^{x+2}-5^x }{5^x\times4}[/tex]
Now, we know that,
[tex]a^{m+n} = a^m . a^n[/tex]
Then,
[tex]5^{x+2}=5^x . 5^2[/tex]
So,
[tex]\frac{5^{x+2}-5^x}{5^x\times4}=\frac{5^x.5^2-5^x}{5^x\times4}[/tex]
Now, taking [tex]5^{x}[/tex] common from the numerator of the given expression, then
[tex]\frac{5^{x+2}-5^x}{5^x\times4}=\frac{5^x(5^2-1)}{5^x\times4}[/tex]
[tex]\implies\frac{5^{x+2}-5^x }{5^x\times4}=\frac{5^2-1}{4}[/tex]
[tex]\implies\frac{5^{x+2}-5^x}{5^x\times4}=\frac{5\times5-1}{4}=\frac{25-1}{4}[/tex]
[tex]\implies\frac{5^{x+2}-5^x}{5^x\times4}=\frac{24}{4}=6[/tex]
So, the simplified form of the given expression gives the result 6.
