Viết các tích sau dưới dạng lũy thừa :
a) \(18^{20}.45^5.5^{25}.8^{10}\)
b) \(\left(x^2.y\right)^5.\left(x^2.y^2\right)^7.\left(x.y\right)^6.x^3\)
c) \(2^7.3^8.4^9.9^8\)
LM ĐẦY ĐỦ GIÚP MK NHÉ ! AI NHANH MK TK !
Viết các tích dưới dạng lũy thừa :
a) \(18^{20}.45^5.5^{25}.8^{10}\)
b) \(\left(x^2.y\right)^5.\left(x^2.y^2\right)^7.\left(xy\right)^6.x^3\)
c) \(2^7.3^8.4^9.9^8\)
\(a)18^{20}.45^5.5^{25}.8^{10}\)
\(=\left(2.3^2\right)^{20}.\left(3^2.5\right)^5.5^{25}.\left(2^3\right)^{10}\)
\(=2^{20}.3^{40}.3^{10}.5^5.5^{25}.2^{30}\)
\(=2^{50}.3^{50}.5^{30}\)
\(=6^{50}.5^{30}\)
\(=\left(6^5\right)^{10}.\left(5^3\right)^{10}\)
\(=7776^{10}.125^{10}\)
\(=972000^{10}\)
\(b)\left(x^2.y\right)^5.\left(x^2.y^2\right)^7.\left(xy\right)^6.x^3\)
\(=x^{10}.y^5.x^{14}.y^{14}.x^6.y^6.x^3\)
\(=x^{33}.y^{25}\)
\(=x^{25}.y^{25}.x^8\left(?\right)\)
\(c)2^7.3^8.4^9.9^8\)
\(=2^7.3^8.\left(2^2\right)^9.\left(3^2\right)^8\)
\(=2^7.3^8.2^{18}.3^{16}\)
\(=2^{25}.3^{24}\)\(\left(?\right)\)
Viết các tích sau dưới dạng lũy thừa :
a) \(3^5.5^7.45\)
b) \(2^8.4^5.9^9\)
c) \(\left(2^3.3^5.5^7\right)^{10}.12^{20}\)
d) \(\left(x^2.y\right)^5.\left(x^2.y^2\right)^7.\left(x.y^2\right)^6.x^3\)
e) \(18^{20}.45^5.5^{25}.8^{10}\)
f) \(2^7.3^8.4^9.9^8\)
CÁC BN GIÚP MK VS !
a)\(3^5.5^7.45=3^5.5^7.3^2.5=3^7.5^8\)
b)\(2^8.4^5.9^9\)\(=2^8.2^{10}.9^9=2^{18}.9^9\)
c)\(\left(2^3.3^5.5^7\right)^{10}.12^{20}=2^{13}.3^{15}.5^{17}.12^{20}\)\(=2^{13}.3^{15}.5^{17}.2^{40}.3^{20}=2^{53}.3^{35}.5^{17}\)
d)\(\left(x^2y\right)^5.\left(x^2y^2\right)^7.\left(x.y^2\right)^6.x^3=x^{10}.y^5.x^{14}.y^{14}.x^6.y^{12}.x^3\)
\(=x^{33}.y^{31}\)
e)\(18^{20}.45^5.5^{25}.8^{10}=2^{20}.3^{40}.5^5.3^{10}.5^5.5^{25}.2^{30}\)
\(=2^{50}.3^{50}.5^{35}=6^{50}.5^{35}\)
f)\(2^7.3^8.4^9.9^8=2^7.3^8.2^{18}.3^{16}=2^{25}.3^{24}\)
Viết các tích sau dưới dạng lũy thừa :
a) \(3^5.5^7.45\)
b) \(2^8.4^5.9^9\)
c) \(\left(2^3.3^5.5^4\right)^{10}.12^{20}\)
GIẢI ĐẦY ĐỦ NHA ! AI NHANH MK TK ! ^-<
a,ta có:
\(3^5.5^7.5.3^2\)
\(=\left(3^5.3^2\right).\left(5.5^7\right)\)
\(=3^7.5^8\)
\(b=2^8.\left(2.2\right)^5.9^9\)
\(=2^8.2^{10}.9^9\)
\(=2^{18}.9^9\)
Mn giúp em với:
1. Tìm các số tự nhiên x ; y biết \(\left(x+5\right)\cdot\left(2y+1\right)=42\)
2. Tìm số tự nhiên x biết: \(\left(x+20\right)⋮10;\left(x-15\right)⋮5;\left(x+18\right)⋮9;x⋮8;x< 500\)
3. Tìm 2 số tự nhiên a ; b biết \(a-b=6\)và \(BCNN\left(a;b\right)=180\)
Mn giải đầy đủ giúp em ạ
1 .x+5 và 2y+1 là Ư(42) lập bảng tính
2.vd tc chia hết
Phân tích các đa thức sau thành phân tử:
a) \(125x^3+y^6\)
b) \(5xy^2-10xyz+5xz^2\)
c) \(3x^2\left(a+b+c\right)+36xy\left(a+b+c\right)+108y^2\left(a+b+c\right)\)
d) \(\left(4x-8\right)\left(x^2+6\right)-\left(4x-8\right)\left(x+7\right)+9\left(8-4x\right)\)
e) \(100x^2-\left(x^2+25\right)^2\)
f) \(\left(x-y+5\right)^2-2\left(x-y+5\right)+1\)
a)ta co: 125x^3+y^6=(5x)^3+(y^2)^3=(5x+y^2)(5x-5xy^2+y^2) b)ta co 5xy^2-10xyz+5xz^2=5x(y^2-2yz+z^2)=5x(y-z)^2 (may cau sau gan giong ban tu lam nha)
b) \(5xy^2-10xyz+5xz^2\)
\(=5xy^2-5xyz-5xyz+5xz^2\)
\(=5xy\left(y-z\right)-5xz\left(y-z\right)\)
\(=\left(y-z\right)\left(5xy-5xz\right)\)
\(=5x\left(y-z\right)\left(y-z\right)\)
\(=5x\left(y-z\right)^2\)
c) \(3x^2\left(a+b+c\right)+36xy\left(a+b+c\right)+108y^2\left(a+b+c\right)\)
\(=\left(a+b+c\right)\left(3x^2+36xy+108y^2\right)\)
\(=\left(a+b+c\right)\left(\sqrt{3x}+6\sqrt{3y}\right)^2\)
2) CMR
\(\left(ax+by\right)^2\le\left(a^2+b^2\right)\left(x^2+y^2\right)\forall a,b,x,y\)
lm nhanh giúp mk nhé mk đang cần gấp
(a² + b²)(c² + d²) ≥ (ac + bd)² \(\forall a,b,c,d\)
↔ (ac)² + (ad)² + (bc)² + (bd)² ≥ (ac)² + 2abcd + (bd)² \(\forall a,b,c,d\)
↔ (ad)² + (bc)² ≥ 2abcd \(\forall a,b,c,d\)
↔ (ad)² - 2abcd + (bc)² ≥ 0 \(\forall a,b,c,d\)
↔ (ad - bc)² ≥ 0 \(\forall a,b,c,d\)
=> luôn đúng
Vậy.....
!Chúc Bạn Học Tốt!
rút gọn
A=\(\dfrac{8+x\left(1+\sqrt{x-2\sqrt{x}+1}\right)}{\left(x-4\right)\left(x-2\sqrt{x}+4\right)}+\dfrac{x-3\sqrt{x}}{2\left(x-\sqrt{x}-6\right)}\)
lm nhanh giúp mk nhé
Ta có: \(\dfrac{8+x\left(1+\sqrt{x-2\sqrt{x}+1}\right)}{\left(x-4\right)\left(x-2\sqrt{x}+4\right)}+\dfrac{x-3\sqrt{x}}{2\left(x-\sqrt{x}-6\right)}\)
\(=\dfrac{8+x\left(1+\sqrt{x}-1\right)}{\left(x-4\right)\left(x-2\sqrt{x}+4\right)}+\dfrac{\sqrt{x}\left(\sqrt{x}-3\right)}{2\left(\sqrt{x}-3\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{x\sqrt{x}+8}{\left(x-4\right)\left(x-2\sqrt{x}+4\right)}+\dfrac{\sqrt{x}}{2\left(\sqrt{x}+2\right)}\)
\(=\dfrac{\sqrt{x}+2}{x-4}+\dfrac{\sqrt{x}}{2\left(\sqrt{x}+2\right)}\)
\(=\dfrac{1}{\sqrt{x}-2}+\dfrac{\sqrt{x}}{2\left(\sqrt{x}+2\right)}\)
\(=\dfrac{2\left(\sqrt{x}+2\right)+\sqrt{x}\left(\sqrt{x}-2\right)}{2\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)
\(=\dfrac{2\sqrt{x}+4+x-2\sqrt{x}}{2\left(x-4\right)}\)
\(=\dfrac{x+4}{2x-8}\)
1.Tìm x
a) x: \(\left(\dfrac{3}{4}\right)^3\) = \(\left(\dfrac{3}{4}\right)^2\)
b) \(\left(\dfrac{2}{5}\right)^5\) . x = \(\left(\dfrac{2}{5}\right)^8\)
2. Viết các số : (0.36)\(^8\) và (0.216)\(^4\) dưới dạng lũy thừa của cơ số 0,6
1.
a) x : \(\left(\dfrac{3}{4}\right)^3\) =\(\left(\dfrac{3}{4}\right)^3\)
x = \(\left(\dfrac{3}{4}\right)^3.\left(\dfrac{3}{4}\right)^3\)
x = \(\dfrac{3}{4}^{3+3}\)
x = \(\dfrac{3}{4}^6\)
x = \(\dfrac{729}{4096}\)
b) \(\left(\dfrac{2}{5}\right)^5.x=\left(\dfrac{2}{5}\right)^8\)
x = \(\left(\dfrac{2}{5}\right)^8:\left(\dfrac{2}{5}\right)^5\)
x = \(\dfrac{2}{5}^{8-5}\)
x = \(\dfrac{2}{5}^3\)
x = \(\dfrac{8}{5}\)
2.
(0,36)\(^8\) \([\left(0,6\right)^3]^8\) = (0,6)\(^{3.8}\) = ( 0,6)\(^{24}\)
( 0,216)\(^4\) = \([\left(0,6\right)^3]^4\) = (0.6)\(^{3.4}\) = ( 0,6)\(^{12}\)
\(x:\left(\dfrac{3}{4}\right)^3=\left(\dfrac{3}{4}\right)^2\)
\(x=\left(\dfrac{3}{4}\right)^2.\left(\dfrac{3}{4}\right)^3\) <=> \(x=\left(\dfrac{3}{4}\right)^{2+3}\)
=> \(x=\left(\dfrac{3}{4}\right)^5\)
b, \(\left(\dfrac{2}{5}\right)^5.x=\left(\dfrac{2}{5}\right)^8\)
\(x=\left(\dfrac{2}{5}\right)^8:\left(\dfrac{2}{5}\right)^5\Leftrightarrow x=\left(\dfrac{2}{5}\right)^{8-5}\)
=>\(x=\left(\dfrac{2}{5}\right)^3\)
bài 2 : Với bài này ta cần áp dụng quy tắc: \(\left(x^m\right)^n=x^{m.n}\)
\(0,36^8=\left[\left(0,6\right)^2\right]^8=\left(0,6\right)^{16}\)
\(0,216^4=\left[\left(0,6\right)^3\right]^4=\left(0,6\right)^{12}\)
Viết các tích sau dưới dạng một lũy thừa :
a) \(\left(-5\right).\left(-5\right).\left(-5\right).\left(-5\right).\left(-5\right)\)
b) \(\left(-2\right).\left(-2\right).\left(-2\right).\left(-3\right).\left(-3\right).\left(-3\right)\)
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