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a) \(\left(-8\right).\left(-3\right)^3.\left(+125\right)\\ =\left(-2\right)^3.\left(-3\right)^3.\left(+5\right)^3\\ =\left[\left(-2\right).\left(-3\right).\left(+5\right)\right]^3\\ =30^3\)
b) \(27.\left(-2\right)^3.\left(-7\right).\left(+49\right)\\ =3^3.\left(-2\right)^3.\left(-7\right).\left(-7\right)^2\\ =\left[3.\left(-2\right)\right]^3.\left[\left(-7\right).\left(-7\right)^2\right]\\ =\left(-6\right)^3.\left(-7\right)^3\\ =\left[\left(-6\right).\left(-7\right)\right]^3\\ =42^3\)
Giải
a) (−8).(−3)3.(+125)(−8).(−3)3.(+125)
= [(−2).(−2).(−2)].[(−3).(−3).(−3)].(5.5.5)[(−2).(−2).(−2)].[(−3).(−3).(−3)].(5.5.5)
= [(−2).(−3).5].[(−2).(−3).5].[(−2).(−3).5][(−2).(−3).5].[(−2).(−3).5].[(−2).(−3).5]
= 30.30.30=30330.30.30=303
b) 27.(−2)3.(−7).(+49)27.(−2)3.(−7).(+49)
= (3.3.3).[(−2).(−2).(−2)].[(−7).(−7).(−7)](3.3.3).[(−2).(−2).(−2)].[(−7).(−7).(−7)]
= [3.(−2).(−7)].[3.(−2).(−7)].[3.(−2).(−7)][3.(−2).(−7)].[3.(−2).(−7)].[3.(−2).(−7)]
= 42.42.42=423
Trả lời :
( - 8 ) . ( -3 ) . ( + 125 )
=( -2)3. ( -3 ) 1 . 53
Học tốt !
\(25^6.125^3\)
\(=\left(5^2\right)^6.\left(5^3\right)^3\)
\(=5^{12}.5^9\)
\(=5^{12+9}\)
\(=5^{21}\)
Ủng hộ nha
\(a,\left(-7\right).\left(-7\right).\left(-7\right).\left(-7\right)\)
\(=\left(-7\right)^4=2401\)
\(b,\left(-3\right).\left(-3\right).\left(-3\right).\left(-4\right).\left(-4\right).\left(-4\right)\)
\(=\left(-3\right)^3.\left(-4\right)^3=12^3\)
\(c,4.9.25\)
\(=9.\left(4.25\right)=900=30^2\)
\(d,8.\left(-3\right)^3.\left(-125\right)\)
\(=\left(-3\right)^3.\left[\left( -125\right).8\right]\)
\(=\left(-3\right)^3.\left(-1000\right)\)
\(=\left(-3\right)^3.\left(-10\right)^3\)
\(=30^3\)
a. \(\left(-8\right).\left(-3\right)^3.125=\left(-2\right)^3.\left(-3\right)^3.5^3=\left[\left(-2\right).\left(-3\right).5\right]^3=30^3\)
b. \(27.\left(-2\right)^3.\left(-7\right).49=3^3.\left(-2\right)^3.\left(-7\right)^3=\left[3.\left(-2\right).\left(-7\right)\right]^3=42^3\)
a)=(-2)3.(-3)3.53
=[(-2)(-3)5]2
=303
b)=33.(-2)3.(-7)(-7)2
=33.(-2)3.(-7)3
=[3(-2)(-7)]3
=423
a)\(4^3.2^4\div\left(4^2.\frac{1}{32}\right)\)
\(=\left(2^2\right)^3.2^4\div\left(2^2\right)^2\div32\).
\(=2^{\left(2.3\right)}.2^4\div2^{\left(2.2\right)}\div2^5\)
\(=2^6.2^4\div2^4\div2^5\)
\(=2^{6+4-4-5}=2^1\)
b)\(\left(\frac{1}{5}\right)^5=\frac{1}{5^5}=\left|5^5\right|=5^{-5}\)
\(\frac{1}{125}=\frac{1}{5^3}=\left|5^3\right|=5^{-3}\)
c)\(\frac{4}{25}=\frac{2^2}{5^2}=\left(\frac{2}{5}\right)^2=0,4^2\)
\(\frac{-8}{125}=\frac{-2^3}{5^3}=\left(\frac{-2}{5}\right)^2=-0,4^3=0,4^{-3}\)
\(\frac{16}{625}=\frac{2^4}{5^4}=\left(\frac{2}{5}\right)^4=0,4^4\)
Viết các biêu thức sau dưới dạng lũy thừa của một số nguyên:
a,\(12^3:\left(\frac{1}{3}.4.64\right)\)
\(12^3:\left(\frac{1}{3}.4.64\right)=12^3.3.\frac{1}{2^2}.\frac{1}{4^3}=\frac{12^3}{4^3}.3.\frac{1}{2^2}=3^3.3.\frac{1}{2^2}=\frac{3^4}{2^2}=\frac{9^2}{2^2}=\left(\frac{9}{2}\right)^2\)
K viết được dưới dạng số nguyên
− 8 . − 3 3 . + 125 = − 2 3 . − 3 3 .5 3 = − 2. − 3 .5 3 = 30 3