Question

Viết các biểu thức số sau dưới dạng \(a^n,\left(a\in\mathbb{Q},n\in\mathbb{N}\right)\) :

a) \(9.3^3.\dfrac{1}{81}.3^2\)

b) \(4.2^5:\left(2^3.\dfrac{1}{16}\right)\)

c) \(3^2.2^5.\left(\dfrac{2}{3}\right)^2\)

d) \(\left(\dfrac{1}{3}\right)^2.\dfrac{1}{3}.9^2\)

Answer 1

a) \(3^3\)

b)\(2^8\)

c) \(2^7\)

d) \(3^1\)

Answer 2

a) 9.3³.\(\dfrac{1}{81}\) .3² = 3². 3³.\(\dfrac{1}{3^4}\) . 3² = 3³

b) 4. 2⁵: \(\) (2³.\(\dfrac{1}{16}\))= 2². 2⁵: 2³. \(\dfrac{1}{2^4}\) = 2⁷: \(\dfrac{1}{2}\) = 2⁷. 2= 2⁸

c) 3². 2⁵. \(\left(\dfrac{2}{3}\right)^2\) = 3². 2⁵. \(\dfrac{2^2}{3^2}\) = 2⁵. 2² = 2⁷

d) \(\left(\dfrac{1}{3}\right)^2\) .\(\dfrac{1}{3}\) . 9² = \(\dfrac{1}{9}.\dfrac{1}{3}\). 9² = \(\dfrac{9}{3}\) = 3¹

Answer 3

a không bít !

b chịu

c quên rồi

d . . .

Answer 4

a) \(9.3^3.\dfrac{1}{81}.3^2\)

\(=3^2.3^3.3^2.\dfrac{1}{3^4}\)

\(=\dfrac{3^{2+3+2}}{3^4}\)

\(=\dfrac{3^7}{3^4}\)

\(=3^3\)

b) \(4.2^5:\left(2^3.\dfrac{1}{16}\right)\)

\(=2^2.2^5:\left(2^3.\dfrac{1}{2^4}\right)\)

\(=2^{2+5}:\dfrac{2^3}{2^4}\)

\(=2^7:\dfrac{1}{2}=2^7.2=2^8\)

Answer 5

a)

\(9.3^3.\dfrac{1}{81}.3^2\\ =3^2.3^3.\left(\dfrac{1}{3}\right)^4.3^2\\ =\dfrac{3^7}{3^4}\\ =3^3\)

b)

\(4.2^5:\left(2^3.\dfrac{1}{16}\right)\\ =2^2.2^5:\left(2^3.\dfrac{1}{2^4}\right)\\ =2^7:\dfrac{2^3}{2^4}\\ =2^7.\dfrac{2^4}{2^3}\\ =2^7.2=2^8\)

c)

\(3^2.2^5.\left(\dfrac{2}{3}\right)^2\\ =3^2.2^5.\dfrac{2^2}{3^2}\\ =2^{5+2}\\ =2^7\)

d)

\(\left(\dfrac{1}{3}\right)^2.\dfrac{1}{3}.9^2\\ \left(\dfrac{1}{3}\right)^2.\dfrac{1}{3}.\left(3^2\right)^2\\ =\dfrac{1}{3^2}.\dfrac{1}{3}.3^4\\ =\dfrac{3^4}{3^{2+1}}\\ =\dfrac{3^4}{3^3}\\ =3\)

Answer 6