Bài $ 5 $)
$ a $) ( $\frac{1}{3}$ ) $^{1}$ – ( – $\frac{6}{7}$ ) $^{0}$ + ( $\frac{1}{2}$) $^{2}$ : $ 2 $
$ b $) $\frac{3^{6}. 45^{4}- 15^{13} : 5^{-9} }{ 27^{4}. 25^{3} + 45^{6} }$
Bài $ 5 $)
$ a $) ( $\frac{1}{3}$ ) $^{1}$ – ( – $\frac{6}{7}$ ) $^{0}$ + ( $\frac{1}{2}$) $^{2}$ : $ 2 $
$ b $) $\frac{3^{6}. 45^{4}- 15^{13} : 5^{-9} }{ 27^{4}. 25^{3} + 45^{6} }$
a) $\Bigg(\dfrac{1}{3}\Bigg)^1-\Bigg(-\dfrac{6}{7}\Bigg)^0+\Bigg(\dfrac{1}{2}\Bigg)^2:2$
$=\dfrac{1}{3}-1+\dfrac{1}{4}:2$
$=-\dfrac{2}{3}+\dfrac{1}{8}$
$=-\dfrac{13}{24}$
b) $\dfrac{3^6.45^4-15^{13}:5^{-9}}{27^4.25^3+45^6}$
$=\dfrac{3^6.(3^2.5)^4-5^{13}.3^{13}:5^{-9}}{(3^3)^4.(5^2)^3+(3^2.5)^6}$
$=\dfrac{3^{14}.5^4-5^{22}.3^{13}}{3^{12}.5^6.2}$
$=\dfrac{3^{13}.5^4(3-5^{18})}{3^{12}.5^6.2}$
$=\dfrac{3(3-5^{18})}{2.5^2}$
$=\dfrac{9-3.5^{18}}{50}$
a, $($\frac{1}{3}$)^{1}$ – $($\frac{-6}{7}$)^{0}$ + ($\frac{1}{2}$)² : 2
= $\frac{1}{3}$ – 1 + $\frac{1}{4}$ : 2
= $\frac{1}{3}$ – 1 + $\frac{1}{4}$ . $\frac{1}{2}$
= $\frac{1}{3}$ – 1 + $\frac{1}{8}$
= $\frac{8 – 24 + 3}{24}$
= $\frac{-13}{24}$
b, $\frac{3^{6}.45^{4} – 15^{3}:5^{-9}}{27^{4}.25^{3}+45^{6}}$
= $\frac{3^{6}.(3^{2}.5)^{4}-3^{13}.5^{13}:5^{-9}}{(3^{3})^{4}.(5^2)^{3}+(5.3^2)^6}$
= $\frac{3^{6}.3^{8}.5^{4}-3^{13}.5^{13}:5^{-9}}{3^{12}.5^6+5^6.3^{12}}$
= $\frac{3^{14}.5^{4}-3^{13}.5^{22}}{2.3^{12}.5^6}$
= $\frac{3^{13}.5^{4}(3-5^{18})}{2.3^{12}.5^6}$
= $\frac{3.(3-5^{18})}{2.5^2}$
= $\frac{3.(3-5^{18})}{2.25}$
= $\frac{9 – 3.5^{18}}{50}$
Chúc bạn học tốt ^^