Question

Tính nhanh

\(\frac{4^6.3^4.9^5}{6^{12}}\)

\(\frac{3^{10}.11+9^5.5}{3^9.2^4}\)

2¹⁰⁰-2⁹⁹-2⁹⁸-..-2²-2

3⁸:3⁶+(2²)⁴:2⁹

Answer 1

\(\frac{4^6.3^4.9^5}{6^{12}}=\frac{\left(2^2\right)^6.3^4.\left(3^2\right)^5}{\left(2.3\right)^{12}}=\frac{2^{12}.3^4.3^{10}}{2^{12}.3^{12}}=\frac{2^{12}.3^{14}}{2^{12}.3^{12}}=3^2=9\)​​\(\frac{3^{10}.11+9^5.5}{3^9.2^4}=\frac{3^{10}.11+\left(3^2\right)^5.5}{3^9.16}=\frac{3^{10}.11+3^{10}.5}{3^9.16}=\frac{3^{10}.\left(11+5\right)}{3^9.16}=\frac{3^{10}.16}{3^9.16}=3\)2¹⁰⁰ - 2⁹⁹ - 2⁹⁸ - ... - 2² - 2

= 2¹⁰⁰ - (2⁹⁹ + 2⁹⁸ + ... + 2² + 2)

Đặt A = 2⁹⁹ + 2⁹⁸ + ... + 2² + 2

2A = 2¹⁰⁰ + 2⁹⁹ + ... + 2³ + 2²

2A - A = (2¹⁰⁰ + 2⁹⁹ + ... + 2³ + 2²) - (2⁹⁹ + 2⁹⁸ + ... + 2² + 2)

A = 2¹⁰⁰ - 2

Ta có:

2¹⁰⁰ - 2⁹⁹ - 2⁹⁸ - ... - 2² - 2

= 2¹⁰⁰ - (2¹⁰⁰ - 2)

= 2¹⁰⁰ - 2¹⁰⁰ + 2

= 0 + 2

= 2

3⁸ : 3⁶ + (2²)⁴ : 2⁹

= 3² + 2⁸ : 2⁹

\(=9+\frac{1}{2}\)

\(=\frac{18}{2}+\frac{1}{2}=\frac{19}{2}\)