Câu 1:
a, $\frac{3^3.3^4}{3^{10}}$= $\frac{3^{7}}{y3^{10}}$ = $\frac{1}{3^{3}}$ = $\frac{1}{27}$
b, $\frac{(0,8)^{2}}{(0,4)^{2}}$ = $\frac{\frac{16}{25}}{\frac{4}{25}}$ = 4
c, $\frac{2³.4²}{8³}$ = $\frac{2³.2^4}{2^9}$ = $\frac{2^{12}}{2^9}$ = 2³ = 8
d, $\frac{27².9}{81}$ = $\frac{27.3.27.3}{81}$ = $\frac{81²}{81}$= 81
Câu 2:
a, $(\frac{1}{2})^{n}$ = $\frac{1}{16}$
⇔ $(\frac{1}{2}^{n}$ = $(\frac{1}{2})^{4}$
⇒ n = 4
b, $(\frac{2}{3})^{n}$ = $\frac{8}{27}$
⇔ $(\frac{2}{3}^{n}$ = ($\frac{2}{3}$)³
⇒ n = 3
c, $\frac{6^{n}}{3³.4}$ = 2
⇔ $\frac{6^{n}}{108}$ = 2
⇔ $6^{n}$ = 216
⇔ $6^{n} = 6³
⇒ n = 3
Câu 3:
b, $6^{4}$ . 8²
= 36² . 8²
= (36.8)²
= 288²
c, 16 . 81
= $2^{4}$ . $3^{4}$
= $(2.3)^{4}$
= $6^{4}$
d, $25^{4}$ . $2^{8}$
= $5^{8}$ . $2^{8}$
= $(5.2)^{8}$
= $10^{8}$
Câu 4:
a, $27^{4}$ : 9³
= $3^{12}$ : $3^{6}$
= $3^{6}$
= 729
b, $\frac{6².3³}{12²}$
= $\frac{2².3^{5}}{2^{4}.3²}$
= $\frac{3³}{2²}$
= $\frac{27}{4}$
