Question

Vt biểu thức sau dưới dạng lũy thừa của một số hữu tỉ.

a) (2/3)² . 4/9      b) [(13/2)⁵ : 13/2) . 169/4

Answer 1

Làm lại:
\(b,\left[\left(\dfrac{13}{2}\right)^5:\dfrac{13}{2}\right].\dfrac{169}{4}\)
\(=\left[\left(\dfrac{13}{2}\right)^{5-1}\right].\dfrac{169}{4}\)
\(=\left(\dfrac{13}{2}\right)^4.\dfrac{169}{4}\)
\(=\left(\dfrac{13}{2}\right)^4.\dfrac{13^2}{2^2}\)
\(=\left(\dfrac{13}{2}\right)^4.\left(\dfrac{13}{2}\right)^2\)
\(=\left(\dfrac{13}{2}\right)^{4+2}\)
\(=\left(\dfrac{13}{2}\right)^6\)

Answer 2

\(a,\left(\dfrac{2}{3}\right)^2.\dfrac{4}{9}=\left(\dfrac{2}{3}\right)^2.\dfrac{2^2}{3^2}=\left(\dfrac{2}{3}\right)^2.\left(\dfrac{2}{3}\right)^2=\left(\dfrac{2}{3}\right)^{2+2}=\left(\dfrac{2}{3}\right)^4\)
\(b,\left[\left(\dfrac{13}{2}\right)^2:\dfrac{13}{2}\right].\dfrac{169}{4}\)
\(=\left[\left(\dfrac{13}{2}\right)^{2-1}\right].\dfrac{169}{4}\)
\(=\left(\dfrac{13}{2}\right).\dfrac{169}{4}\)
\(=\left(\dfrac{13}{2}\right).\dfrac{13^2}{2^2}\)
\(=\left(\dfrac{13}{2}\right).\left(\dfrac{13}{2}\right)^2\)
\(=\left(\dfrac{13}{2}\right)^{1+2}\)
\(=\left(\dfrac{13}{2}\right)^3\)

Answer 3

`(2/3)^2 . 4/9`

`= (2/3)^2 . (2/3)^2`

`= (2/3)^(2+2)`

`=(2/3)^4 = 16/81`

`[(13/2)^2 : 13/2] . 169/4)`

`= (13/2) . 169/4`

`= 13/2 . (13/2)^2`

`=(13/2)^3`