thực hiện phép tính sau
\(\dfrac{6^6.25^6}{15^5.10^5}\)
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24 tháng 1 2022
=\(\left[\dfrac{\left(0,4.2\right)^5}{\left(0,4\right)^6}+\dfrac{2^9.2^6.3^8}{\left(3.2\right)^6.2^9}\right]=\left[\dfrac{\left(0,4\right)^5.2^5}{\left(0,4\right)^6}+\dfrac{2^6.3^8}{3^6.2^6}\right]\)
=\(\left[\dfrac{2^5}{0,4}+3^2\right]\)
=\(\left[80+9\right]=89\)
R
24 tháng 1 2022
\(\left[\dfrac{\left(2.0,4\right)^5}{0,4,0,4^5}+\dfrac{2^{15}.3^8}{3^6.2^6.2^9}\right]\div\dfrac{3^{20}.5^{30}}{3^{15}.5^{30}}\)
\(=\left[\dfrac{2^5.0.4^5}{0,4.0,4^5}+\dfrac{2^{15}.3^8}{3^6.2^{15}}\right]\div3^5\)
\(=\left[\dfrac{2^5}{0,4}+3^2\right]\div243\)
\(=80+\left(3^5\div3^2\right)\)
\(=80+3^3\)
\(=80+27\)
\(=107\)
31 tháng 7 2018
a) \(\frac{15^5.10^5}{6^6.25^6}\)= (15.10)^5/(6.25)^6=150^5/150^6=1/150
11 tháng 7 2019
\(^{\frac{\left(5^4-5^3\right)^3}{125^4}=\frac{\left[5^3\cdot\left(5-1\right)\right]^3}{\left(5^3\right)^4}=\frac{\left[5^3\cdot4\right]^3}{5^3\cdot4}=\frac{\left(5^3\right)^3\cdot4^3}{5^{12}}=\frac{5^9\cdot4^3}{5^9\cdot5^3}=\frac{4^3}{5^3}}\)
T
4 tháng 10 2023
\(a,\dfrac{15^3}{5^4}\)
\(=\dfrac{\left(3\cdot5\right)^3}{5^4}\)
\(=\dfrac{3^3\cdot5^3}{5^4}\)
\(=\dfrac{3^3}{5}\)
\(=\dfrac{27}{5}\)
\(---\)
\(b,\dfrac{21^3}{7^4}\)
\(=\dfrac{\left(3\cdot7\right)^3}{7^4}\)
\(=\dfrac{3^3\cdot7^3}{7^4}\)
\(=\dfrac{3^3}{7}\)
\(=\dfrac{27}{7}\)
\(---\)
\(c,\dfrac{6^6}{3^8}\)
\(=\dfrac{\left(2\cdot3\right)^6}{3^8}\)
\(=\dfrac{2^6\cdot3^6}{3^8}\)
\(=\dfrac{2^6}{3^2}\)
\(=\dfrac{64}{9}\)
#\(Toru\)
7 tháng 9 2023
\(\dfrac{2}{\sqrt[]{6}-2}+\dfrac{2}{\sqrt[]{6}+2}+\dfrac{5}{\sqrt[]{6}}\)
\(=\dfrac{2}{\sqrt[]{6}-2}+\dfrac{2}{\sqrt[]{6}+2}+\dfrac{5\sqrt[]{6}}{6}\)
\(=\dfrac{12\left(\sqrt[]{6}+2\right)}{6\left(\sqrt[]{6}-2\right)\left(\sqrt[]{6}+2\right)}+\dfrac{12\left(\sqrt[]{6}-2\right)}{6\left(\sqrt[]{6}-2\right)\left(\sqrt[]{6}+2\right)}+\dfrac{5\sqrt[]{6}\left(\sqrt[]{6}-2\right)\left(\sqrt[]{6}+2\right)}{6\left(\sqrt[]{6}-2\right)\left(\sqrt[]{6}+2\right)}\)
\(=\dfrac{12\sqrt[]{6}+24+12\sqrt[]{6}-24+5\sqrt[]{6}\left(6-2\right)}{6\left(6-2\right)}\)
\(=\dfrac{24\sqrt[]{6}+20\sqrt[]{6}}{24}\)
\(=\dfrac{44\sqrt[]{6}}{24}\)
\(=\dfrac{11\sqrt[]{6}}{6}\)
H9
HT.Phong (9A5)
CTVHS
8 tháng 9 2023
\(B=\left(\dfrac{4}{1-\sqrt{5}}+\dfrac{1}{2+\sqrt{5}}-\dfrac{4}{3-\sqrt{5}}\right)\left(\sqrt{5}-6\right)\)
\(B=\left[\dfrac{4\left(1+\sqrt{5}\right)}{\left(1-\sqrt{5}\right)\left(1+\sqrt{5}\right)}+\dfrac{2-\sqrt{5}}{\left(2+\sqrt{5}\right)\left(2-\sqrt{5}\right)}-\dfrac{4\left(3+\sqrt{5}\right)}{\left(3-\sqrt{5}\right)\left(3+\sqrt{5}\right)}\right]\left(\sqrt{5}-6\right)\)
\(B=\left[\dfrac{4\left(1+\sqrt{5}\right)}{1-5}+\dfrac{2-\sqrt{5}}{4-5}-\dfrac{4\left(3+\sqrt{5}\right)}{9-5}\right]\left(\sqrt{5}-6\right)\)
\(B=\left[-\dfrac{4\left(1+\sqrt{5}\right)}{4}-\dfrac{2-\sqrt{5}}{1}-\dfrac{4\left(3+\sqrt{5}\right)}{4}\right]\left(\sqrt{5}-6\right)\)
\(B=\left(-1-\sqrt{5}-2+\sqrt{5}-3-\sqrt{5}\right)\left(\sqrt{5}-6\right)\)
\(B=\left(-\sqrt{5}-6\right)\left(\sqrt{5}-6\right)\)
\(B=-\left(\sqrt{5}+6\right)\left(\sqrt{5}-6\right)\)
\(B=-\left(5-36\right)\)
\(B=-\left(-31\right)\)
\(B=31\)
_____________________________
\(\sqrt{48}-\dfrac{\sqrt{21}-\sqrt{15}}{\sqrt{7}-\sqrt{5}}+\dfrac{2}{\sqrt{3}+1}\)
\(=4\sqrt{3}-\dfrac{\sqrt{3}\left(\sqrt{7}-\sqrt{5}\right)}{\sqrt{7}-\sqrt{5}}+\dfrac{2\left(\sqrt{3}-1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}\)
\(=4\sqrt{3}-\sqrt{3}-\dfrac{2\left(\sqrt{3}-1\right)}{2}\)
\(=3\sqrt{3}-\sqrt{3}+1\)
\(=2\sqrt{3}+1\)
VD
21 tháng 3 2022
\(a,\dfrac{-8}{15}+\dfrac{13}{30}-\dfrac{5}{12}=\dfrac{-32}{60}+\dfrac{26}{60}-\dfrac{25}{60}=-\dfrac{31}{60}\\ b,\dfrac{3}{2}.\dfrac{7}{2}+\left(\dfrac{-5}{6}+\dfrac{1}{10}:\dfrac{11}{30}\right)=\dfrac{21}{4}+\left(\dfrac{-5}{6}+\dfrac{3}{11}\right)=\dfrac{21}{4}+\dfrac{-37}{66}=\dfrac{619}{132}\)
\(c,\dfrac{-20}{21}.\dfrac{22}{35}+\dfrac{-20}{21}.\dfrac{13}{35}+\dfrac{-22}{21}=\dfrac{-20}{21}\left(\dfrac{22}{35}+\dfrac{13}{35}\right)+\dfrac{-22}{21}=\dfrac{-20}{21}.1+\dfrac{-22}{21}=\dfrac{-20}{21}+\dfrac{-22}{21}=\dfrac{-42}{21}=-2\)
S
2
A
21 tháng 6 2018
\(\frac{15^5.10^5}{6^6.25^6}\)
\(=\frac{3^5.5^5.2^5.5^5}{3^6.2^6.5^{12}}\)
\(=\frac{3^5.2^5.5^{10}}{3^6.2^6.5^{12}}\)
\(=\frac{1}{3.2.5^2}\)
\(\frac{\left(5^4.5^3\right)^3}{125^4}\)
\(=\frac{\left(5^7\right)^3}{5^{12}}\)
\(=\frac{5^{21}}{5^{12}}\)
\(=5^9\)
AH
Akai Haruma
Giáo viên
31 tháng 12 2020
Lời giải:
\(\left(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{16}-2}-\frac{12}{3-\sqrt{16}}\right).(\sqrt{6}+11)=\left(\frac{15(\sqrt{6}-1)}{(\sqrt{6}+1)(\sqrt{6}-1)}+\frac{4}{4-2}-\frac{12}{3-4}\right)(\sqrt{6}+11)\)
\(=\left(\frac{15(\sqrt{6}-1)}{6-1}+2+12\right)(\sqrt{6}+11)=(3\sqrt{6}-3+14)(\sqrt{6}+11)\)
\(=(3\sqrt{6}+11)(\sqrt{6}+11)\)
\(\dfrac{6^6\cdot25^6}{15^5\cdot10^5}=\dfrac{\left(6\cdot25\right)^6}{\left(15\cdot10\right)^5}=\dfrac{150^6}{150^5}=150\)