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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) \(27.\left(-2\right)^3.\left(-7\right).\left(+49\right)\\ =3^3.\left(-2\right)^3.\left(-7\right).\left(-7\right)^2\\ =\left[3.\left(-2\right)\right]^3.\left[\left(-7\right).\left(-7\right)^2\right]\\ =\left(-6\right)^3.\left(-7\right)^3\\ =\left[\left(-6\right).\left(-7\right)\right]^3\\ =42^3\)
a) Ta thấy: có 5 thừa số (-5) nên tích mang dấu "-" nên:
(-5).(-5).(-5).(-5).(-5) = -55
b) (-2).(-2).(-2).(-3).(-3).(-3)
= (-2).(-3).(-2).(-3).(-2).(-3)
=6.6.6 = 63
hoặc: ta thấy tích có 6 thừa số nguyên âm nên tích mang dấu "+"
(-2).(-2).(-2).(-3).(-3).(-3)
= 23.33
a: \(=\dfrac{3^3\cdot2^6}{3^{-4}\cdot2^6}=3^7\)
b: \(=\left(\dfrac{3}{7}\right)^5\cdot\left(\dfrac{3}{7}\right)\cdot\dfrac{5^6}{3^6}:\left(\dfrac{625}{343}\right)^2\)
\(=\dfrac{3^6}{7^6}\cdot\dfrac{5^6}{3^6}:\dfrac{5^8}{7^6}\)
\(=\dfrac{1}{5^2}\)
c: \(=5^{4+3}\cdot\left(\dfrac{5}{2}\right)^{-5}\cdot\dfrac{1}{25}\)
\(=5^5\cdot\left(\dfrac{2}{5}\right)^5=2^5\)
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)\(\frac{4}{25}=\frac{2^2}{5^2}=\left(\frac{2}{5}\right)^2=0,4^2\)
\(\frac{-8}{125}=\frac{-2^3}{5^3}=\left(\frac{-2}{5}\right)^2=-0,4^3=0,4^{-3}\)
\(\frac{16}{625}=\frac{2^4}{5^4}=\left(\frac{2}{5}\right)^4=0,4^4\)
a) 123 : ( 3-4 x 64 )
= 1728 : ( \(\frac{1}{81}\)x 64)
= 1728 : \(\frac{64}{81}\)
= 2187 = 37
\(2a^3x^2y.8a^2x^3y^4.16a^3x^3y^3\)
\(=16^2.a^8.x^8.y^8\)
\(=\left(2axy\right)^8\)
a (-7)^6
b (-4).(-4).(-4).(-5).(-5).(-5)
=[(-4).(-5)].[(-4).(-5)].[(-4).(-5)]
=20 .20 .20 =20^3
a) \(\left(-7\right).\left(-7\right).\left(-7\right).\left(-7\right).\left(-7\right).\left(-7\right)=\left(-7\right)^6\)
b) \(\left(-4\right).\left(-4\right).\left(-4\right).\left(-5\right).\left(-5\right).\left(-5\right)\\ =\left[\left(-4\right).\left(-5\right)\right].\left[\left(-4\right).\left(-5\right)\right].\left[\left(-4\right).\left(-5\right)\right]\\ =20.20.20=20^3\)
Câu 1 :
a) \(4.\left(\frac{1}{32}\right)^{-2}:\left(2^3.\frac{1}{16}\right)\)
\(=2^2.32^2:\left(\frac{1}{8}.16\right)=\left(2.32\right)^2:2=64^2:2\)
\(=2048=2^{11}\)
b) \(5^2.3^5.\left(\frac{3}{5}\right)^2\)
\(=\left(5.\frac{3}{5}\right)^2.3^5=3^2.3^5=3^7\)
VIẾT CÁC BIỂU THỨC DƯỚI DẠNG LUỸ THỪA CỦA 1 SỐ HỮU TỈ
\(a,4\cdot\left(\frac{1}{32}\right)^{-2}:\left(2^3\cdot\frac{1}{16}\right)\\ =4\cdot1024:\left(8\cdot\frac{1}{16}\right)\\ =4\cdot1024:\frac{1}{2}\\ =2\cdot1024\\ =2\cdot2^{10}\\ =2^{11}\)
\(b,5^2\cdot3^5\cdot\left(\frac{3}{5}\right)^2\\ =5^2\cdot\left(\frac{3}{5}\right)^2\cdot3^5\\ =3^2\cdot3^5\\ =3^7\)
2 SO SÁNH
\(a,10^{20}\text{ và }9^{10}\)
Có: \(9^{10}=\left(3^2\right)^{10}=3^{20}\)
\(\Rightarrow10^{20}>3^{20}\\ \text{hay}\text{ }10^{20}>9^{10}\)
\(b,\left(-5\right)^3\text{ và }\left(-3\right)^{50}\)
Có: \(\left(-3\right)^{50}=3^{50}\)
\(\Rightarrow\left(-5\right)^3< 3^{50}\\ \text{hay }\left(-5\right)^3< \left(-3\right)^{50}\)
\(c,64^3\text{ và }16^{12}\)
Có: \(64^3=\left(4^3\right)^3=4^9;16^{12}=\left(4^2\right)^{12}=4^{24}\)
\(\Rightarrow4^9< 4^{24}\\ hay\text{ }64^3< 16^{12}\)
\(d,\left(\frac{1}{16}\right)^{10}\text{ và }\left(\frac{1}{2}\right)^{50}\)
Có: \(\left(\frac{1}{2}\right)^{50}=\left(\frac{1}{2}\right)^{5\cdot10}=\left[\left(\frac{1}{2}\right)^5\right]^{10}=\left(\frac{1}{32}\right)^{10}\)
\(\Rightarrow\left(\frac{1}{16}\right)^{10}>\left(\frac{1}{32}\right)^{10}\\ \text{hay }\left(\frac{1}{16}\right)^{10}>\left(\frac{1}{2}\right)^{50}\)
\(12^3:\left(\frac{1}{3}.4.64\right)=12^3.3.\frac{1}{2^2}.\frac{1}{4^3}=\frac{12^3}{4^3}.3.\frac{1}{2^2}=3^3.3.\frac{1}{2^2}=\frac{3^4}{2^2}=\frac{9^2}{2^2}=\left(\frac{9}{2}\right)^2\)
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