Question

Сократите дробь : 1000^n - 125^n / 4^n+ 2^n + 1 (^n - в n-ной степени. / - деление (огромная черта). Подробно,пожалуйста.

Answer 1

Пожалуйста...............

Answer 2

Simplifying the Fraction

To simplify the given fraction :1000^n - 125^n / 4^n + 2^n + 1 in terms of n, we can use the difference of squares formula, which states that a^2 - b^2 = (a - b)(a + b).

Using this formula, we can simplify the numerator of the fraction 1000^n - 125^n as follows: 1000^n - 125^n = (10^n)^3 - (5^n)^3 = (10^n - 5^n)(10^{2n} + 5^n + 5^{2n}).

Now, let's simplify the denominator 4^n + 2^n + 1.

The given fraction becomes: (10^n - 5^n)(10^{2n} + 5^n + 5^{2n}) / (4^n + 2^n + 1).

Conclusion

The simplified form of the given fraction :1000^n - 125^n / 4^n + 2^n + 1 in terms of n is (10^n - 5^n)(10^{2n} + 5^n + 5^{2n}) / (4^n + 2^n + 1).