Question

1.Tìm x

a) x: \(\left(\dfrac{3}{4}\right)^3\) = \(\left(\dfrac{3}{4}\right)^2\)

b) \(\left(\dfrac{2}{5}\right)^5\) . x = \(\left(\dfrac{2}{5}\right)^8\)

2. Viết các số : (0.36)\(^8\) và (0.216)\(^4\) dưới dạng lũy thừa của cơ số 0,6

Answer 1

1.

a) x : \(\left(\dfrac{3}{4}\right)^3\) =\(\left(\dfrac{3}{4}\right)^3\)

x = \(\left(\dfrac{3}{4}\right)^3.\left(\dfrac{3}{4}\right)^3\)

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

x = \(\dfrac{3}{4}^6\)

x = \(\dfrac{729}{4096}\)

b) \(\left(\dfrac{2}{5}\right)^5.x=\left(\dfrac{2}{5}\right)^8\)

x = \(\left(\dfrac{2}{5}\right)^8:\left(\dfrac{2}{5}\right)^5\)

x = \(\dfrac{2}{5}^{8-5}\)

x = \(\dfrac{2}{5}^3\)

x = \(\dfrac{8}{5}\)

2.

(0,36)\(^8\) \([\left(0,6\right)^3]^8\) = (0,6)\(^{3.8}\) = ( 0,6)\(^{24}\)

( 0,216)\(^4\) = \([\left(0,6\right)^3]^4\) = (0.6)\(^{3.4}\) = ( 0,6)\(^{12}\)

Answer 2

\(x:\left(\dfrac{3}{4}\right)^3=\left(\dfrac{3}{4}\right)^2\)

\(x=\left(\dfrac{3}{4}\right)^2.\left(\dfrac{3}{4}\right)^3\) <=> \(x=\left(\dfrac{3}{4}\right)^{2+3}\)

=> \(x=\left(\dfrac{3}{4}\right)^5\)

b, \(\left(\dfrac{2}{5}\right)^5.x=\left(\dfrac{2}{5}\right)^8\)

\(x=\left(\dfrac{2}{5}\right)^8:\left(\dfrac{2}{5}\right)^5\Leftrightarrow x=\left(\dfrac{2}{5}\right)^{8-5}\)

=>\(x=\left(\dfrac{2}{5}\right)^3\)

bài 2 : Với bài này ta cần áp dụng quy tắc: \(\left(x^m\right)^n=x^{m.n}\)

^{\(0,36^8=\left[\left(0,6\right)^2\right]^8=\left(0,6\right)^{16}\)}

\(0,216^4=\left[\left(0,6\right)^3\right]^4=\left(0,6\right)^{12}\)