Question

[HÀ THỊ LINH CHI]

giúp mk với :

1, tính:

a, 25³:5² ; b, (\(\dfrac{3}{7}\))²¹:(\(\dfrac{9}{49}\))⁶ ; c, 3-(\(\dfrac{-6}{7}\))⁶+(\(\dfrac{1}{2}\))²:2; D, 9.3².\(\dfrac{1}{81}\).3²

^{2, tìm x thuộc Q biết:}

a, 3^x+2=27 ; b, (\(\dfrac{1}{2}\)x-3)⁴=81 ; c, (x-\(\dfrac{1}{2}\))³=-27 ; d, 5.5^x+1=125

Answer 1

[Hải Ngân]

1) Tính

a) 25³ : 5² = (5²)³ : 5² = 5⁶ : 5² = 5⁴ = 625

\(b)\left(\dfrac{3}{7}\right)^{21}:\left(\dfrac{9}{49}\right)^6=\left(\dfrac{3}{7}\right)^{21}:\left[\left(\dfrac{3}{7}\right)^2\right]^6=\left(\dfrac{3}{7}\right)^{21}:\left(\dfrac{3}{7}\right)^{12}=\left(\dfrac{3}{7}\right)^9\) d) 9 . 3² . \(\dfrac{1}{81}\) . 3² = 3² . 3² . \(\dfrac{1}{3^4}\) . 3² = 9

2) Tìm x thuộc Q, biết:

a) 3^{x + 2} = 27

=> 3^{x + 2} = 3³

x + 2 = 3

x = 3 - 2

x = 1

b) \(\left(\dfrac{1}{2}x-3\right)^4=81\)

\(\Rightarrow\left(\dfrac{1}{2}x-3\right)^4=3^4\)

\(\dfrac{1}{2}x-3=3^{ }\)

\(\dfrac{1}{2}x=3+3\)

\(\dfrac{1}{2}x=9\)

\(x=9:\dfrac{1}{2}\)

\(x=18\)

c) \(\left(x-\dfrac{1}{2}\right)^3=-27\)

\(\Rightarrow\left(x-\dfrac{1}{2}\right)^3=\left(-3\right)^3\)

\(x-\dfrac{1}{2}=-3\)

\(x=-3+\dfrac{1}{2}\)

\(x=\dfrac{-5}{2}\)

d) 5 . 5^{x + 1} = 125

5^{x + 1} = 125 : 5

5^{x + 1} = 25

5^{x + 1} = 5²

x + 1 = 2

x = 2 - 1

x = 1.