Question

[Lê Hồng Quỳnh Như]

Giúp mình với ạ

1. Viết biểu thức dưới dạng 1 lũy thừa:

45^10 _x 5³⁰

2. Tìm x, biết:

a) (2x - 1)³ = -8

b) (x + 1/2)² = 1/16

c) (2x +3)² = 9/121

d) (3x - 1)³ = -8/27

4. So sánh:

a)99^2o và 9999¹⁰

b)3⁴⁰⁰⁰ và 9²⁰⁰⁰

c)2³³² và 3²²³

Answer 1

[Hoàng Thị Lan Hương]

1.\(45^{10}.5^{30}=45^{10}.125^{10}=\left(45.125\right)^{10}=5625^{10}\)

2.a. \(\left(2x-1\right)^3=-8\Leftrightarrow\left(2x-1\right)^3=\left(-2\right)^3\)

\(\Leftrightarrow2x-1=-2\Leftrightarrow x=-\frac{1}{2}\)

b.\(\left(x+\frac{1}{2}\right)^2=\frac{1}{16}\Leftrightarrow\orbr{\begin{cases}x+\frac{1}{2}=\frac{1}{4}\\x+\frac{1}{2}=-\frac{1}{4}\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=-\frac{1}{4}\\x=-\frac{3}{4}\end{cases}}\)

c. \(\left(2x+3\right)^2=\frac{9}{121}\Leftrightarrow\orbr{\begin{cases}2x+3=\frac{3}{11}\\2x+3=-\frac{3}{11}\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=-\frac{15}{11}\\x=-\frac{18}{11}\end{cases}}\)

d.\(\left(3x-1\right)^3=-\frac{8}{27}=\left(-\frac{2}{3}\right)^3\)

\(\Leftrightarrow3x-1=-\frac{2}{3}\Leftrightarrow x=\frac{1}{9}\)

4.

a.\(99^{20}=\left(99^2\right)^{10}=9801^{10}\)

Do \(9801^{10}< 9999^{10}\Rightarrow99^{20}< 9999^{10}\)

b.\(3^{4000}=\left(3^2\right)^{2000}=9^{2000}\)

\(\Rightarrow3^{4000}=9^{2000}\)

c.\(2^{332}=\left(2^3\right)^{110}.2^2=8^{110}.4\)

\(3^{223}=\left(3^2\right)^{110}.3^3=\left(3^2\right)^{110}.9=9^{110}.9\)

Ta thấy \(4.8^{110}< 9.9^{110}\)

Vậy \(2^{332}< 3^{223}\)