bài 37:
$a) \frac{4^2.4^3}{2^{10}}=\frac{4^5}{2^{10}}=\frac{2^{10}}{2^{10}}$
$ b) \frac{(0,6)^5}{(0,2)^6}=\frac{3^5.(0,2)^5}{0,2.(0,2)^5}=\frac{3^5}{0,2}$
$=\frac{243}{0,2}=1215$
c) $\frac{2^7.9^3}{6^5.8^2}=\frac{2^2.2^5.3^6}{2^5.3^5.2^6} $
$=\frac{3}{2^4}=\frac{3}{16}$
d) $\frac{6^3+3.6^2+3^3}{-13}+\frac{(2.3)^3+3(2.3)^2+3^3}{-13} $
$ =\frac{2^3.3^3+3.2^2.3^2+3^3}{-13}$
$ =\frac{3^3(2^3+2^2+1}{-13}=-3^3=-27$
bài 38:
a)$2^{27}=2^3.9=(2^3)^9=8^9$
$3^{18}=3^2.9=(3^2)^9=9^9$
b)theo câu a ta có $2^{27}=8^9;3^{18}=9^9$ mà$9^9$ lớn hơn$8^9$\Rightarrow$3^{18} $lớn hơn $2^{27} $
bài 39:
a)$x^{10}=x^7.x^3 b)x^{10}=( x^2)^5 $ c)$x^{10}=\dfrac{x^{12}}{x^2}$
bài 42:
a)$\dfrac{16}{2^n}=2$ \Leftrightarrow $2^n.2=16$ \Leftrightarrow $2^4$ \Leftrightarrow $n+1=4$ \Leftrightarrow $n=3$
b)$\dfrac{(3)^n}{81}=-27$\Leftrightarrow$(-3)^n=(-3)^3.3^4$\Leftrightarrow$(-3)^n=(-3)^7$\Rightarrow$n=7$
c)$\dfrac{8^n}{2^n}=4$\Leftrightarrow$(\dfrac{8}{2})^n=2 ^2$\Leftrightarrow$(2^2)^n=2^2$\Leftrightarrow$n=1$
]bài 44
a)$1.2:3.24=\frac{12}{10}:\frac{324}{100} $
b);c) tương tự
bài 45:
* ta có :$\frac{28}{14}=\frac{8}{4}$
ta có :$3/10=0,3$ (1)
* và $2.1/7 =0,3$ (2)
từ (1)và(2)\Rightarrow$\frac{3}{10}=\frac{2,1}{7}$