Question

Сократите дробь: 10^n+2-10^n-2/10^n

Answer 1

Сорри за подчерк, просто не удобно писать

Answer 2

To simplify the expression $\frac{{10^{n+2}-10^{n-2}}}{{10^n}}$, you can use the properties of exponents. Remember that when you divide two exponential terms with the same base, you can subtract their exponents:

$\frac{{10^{n+2}-10^{n-2}}}{{10^n}} = \frac{{10^{n} \cdot 10^2 - 10^{n} \cdot 10^{-2}}}{{10^n}}$

Now, factor out $10^n$ from the numerator:

$\frac{{10^{n} \cdot (10^2 - 10^{-2})}}{{10^n}}$

Next, cancel out the $10^n$ terms:

$10^2 - 10^{-2} = 100 - \frac{1}{100} = \frac{10000 - 1}{100} = \frac{9999}{100}$

So the simplified fraction is:

$\frac{{10^{n+2}-10^{n-2}}}{{10^n}} = \frac{{9999}}{{100}}$