Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a: \(A=\dfrac{16^5\cdot15^5}{2^{10}\cdot3^5\cdot5^4}=\dfrac{2^{20}\cdot3^5\cdot5^5}{2^{10}\cdot3^5\cdot5^4}=2^{10}\cdot5=5120\)
b: \(B=\dfrac{2^{15}\cdot3+2^{19}\cdot10}{2^{12}\cdot26}=\dfrac{2^{15}\left(3+2^4\cdot10\right)}{2^{13}\cdot13}=2^2\cdot\dfrac{163}{13}=\dfrac{652}{13}\)
a: \(\left(2x-3\right)\cdot12=6^2\)
\(\Leftrightarrow2x-3=3\)
hay x=3
\(a.\) \(\frac{6^3+3.6^2+3^3}{-13}=\frac{2^3.3^3+3.3^2.2^2+3^3}{-13}=\frac{2^3.3^3+3^3.2^2+3^3}{-13}\)
\(=\frac{3^3.\left(2^3+2^2+1\right)}{-13}=\frac{3^3.13}{-13}=\frac{3^3.\left(-1\right)}{1}=-27\)
\(b.\)\(A=2^2+4^2+6^2+...+20^2=2^2\left(1+2^2+3^2+...+10^2\right)\)
\(A=2^2.\frac{10.\left(10+1\right).\left(2.10+1\right)}{6}=4.385=1540\)
( Ta có: công thức tính tổng bình phương liên tiếp tứ 1 đến n là: \(1^2+2^2+3^2+...+n^2=\frac{n\left(n+1\right)\left(2n+1\right)}{6}\))
\(c.\)\(B=100^2+200^2+...+1000^2=\left(100.1\right)^2+\left(100.2\right)^2+...+\left(100.10\right)^2\)
\(B=100^2.1^2+100^2.2^2+...+100^2.10^2=100^2.\left(1^2+2^2+...+10^2\right)\)
Áp dụng công thức \(1^2+2^2+3^2+...+n^2=\frac{n\left(n+1\right)\left(2n+1\right)}{6}\)
Ta có: \(B=100^2\times385=3,850,000\)
=(216+3.36+27):13
=(216+108+27):13
=(324+27):13
=351:13
=27
1-2+3-4+4-5+5-6+...+2015-2016
=(1-2)+(3-4)+(5-6)+...+(2015-2016)
=(-1)+(-1)+(-1)+...+(-1) (có 1008 số hạng)
=(-1)x1008 = -1008
\(\left\{x^2-\left[6^2-\left(8^2-9.7\right)^3-7.5\right]^3-5.3\right\}^3=1\)
\(\Rightarrow\left\{x^2-\left(36-1^3-35\right)^3-15\right\}^3=1\)
\(\Rightarrow x^2-\left(0^3-15\right)^3=1\)
\(\Rightarrow x^2-\left(-3375\right)=1\)
\(\Rightarrow x^2=-3374\)
\(\Rightarrow x\in\varnothing\)
{ x2 - [ 62 - ( 82 - 9.7)3 - 7.5]3 - 5.3 }3 = 1
{ x2 + [ 36 - (64 - 63)3 - 35]3 - 15}3 = 1
[ x2 - ( 36 - 13 - 35 ) - 15 ]3 = 1
[ x2 - ( 36 - 1 - 35 ) - 15]3 = 1
[ x2 - ( 35 - 35 ) - 15]3 = 1
[ x2 - 0 - 15]3 = 1
( x2 - 15 )3 = 1
<=> ( x2 - 15)3 = 13
=> x2 - 15 = 1
<=> x2 = 16
=> x = 4
\(6^3+3.6^2+\frac{3^3}{-13}\)
=\(216+3.36+\frac{27}{-13}\)
\(=216+108+\frac{-27}{13}\)
\(=324+\frac{-27}{13}\)
\(=\frac{4185}{13}\)