((3\(^2\)))\(^2\) - ((-5\(^2\)))\(^2\) + ((-2\(^3\)))\(^2\)

= 81 - 625 + 64

= -544+ 64

= -480

2\(^4\) + 8[(-2)\(^2\) :\(\dfrac{1}{2}\)]\(^0\) - 2\(^{-2}\). 4 + (-2)\(^2\)

= 16+ 8.1 - \(\dfrac{1}{4}\). 4 + 4

= 16+ 8- 1+4

= 27

2\(^4\) + 3(\(\dfrac{1}{2}\))\(^0\) + 2\(^{-2}\).8 + [(-2)\(^3\). \(\dfrac{1}{2^4}\)].2 - \(\dfrac{1}{2}\)

= 16 + 3.1 +\(\dfrac{1}{4}\).8 + [(-8).\(\dfrac{1}{16}\)].2 -\(\dfrac{1}{2}\)

= 16 + 3+ 2 + \(\dfrac{-1}{2}\).2- \(\dfrac{1}{2}\)

= 21 + (-1)- \(\dfrac{1}{2}\)

= 20-\(\dfrac{1}{2}\) = \(\dfrac{40}{2}\) - \(\dfrac{1}{2}\)= \(\dfrac{39}{2}\)

\(\dfrac{15^{10}.5^{10}}{75^{10}}\) + \(\dfrac{\left(0,8\right)^5}{\left(0,4\right)^6}\)

= \(\dfrac{\left(15.5\right)^{10}}{75^{10}}\) + \(\dfrac{\left(0,4.2\right)^5}{\left(0.4\right)^6}\)

= \(\dfrac{75^{10}}{75^{10}}\) + \(\dfrac{\left(0,4\right)^5.2^5}{\left(0,4\right)^6}\)

= 1 + \(\dfrac{2^5}{0,4}\) = 1+ 80 = 81

\(\dfrac{2^{13}.9^4}{6^3.8^3}\)

= \(\dfrac{2^{13}.\left(3^2\right)^4}{\left(2.3\right)^3.\left(2^3\right)^3}\) = \(\dfrac{2^{13}.3^8}{2^3.3^3.2^9}\)

= \(\dfrac{2^4.3^5}{2^3}\) = 2.3\(^5\) = 486

y1 và y2 lần lượt bằng 8 và 6

còn x1, x2 lần lượt bằng -4 và -10

tick nhóe!

ahihi

Đặt \(A=1^2+2^2+3^2+...2015^2\)

\(\Rightarrow A=1.1+2.2+3.3+...+2015.2015\)

\(\Rightarrow A=1\left(2-1\right)+2\left(3-1\right)+3.\left(4-1\right)+...+2015\left(2016-1\right)\)

\(\Rightarrow A=1.2-1+2.3-2+3.4-3+...+2015.2016-2015\)

\(\Rightarrow A=\left(1.2+2.3+3.4+...+2015.2016\right)-\left(1+2+3+...+2015\right)\)

\(\Rightarrow A=\left(1.2+2.3+3.4+...+2015.2016\right)-2031120\)

\(\Rightarrow A+2031120=1.2+2.3+3.4+...+2015.2016\)

\(\Rightarrow3\left(A+2031120\right)=1.2\left(3-0\right)+2.3+\left(4-1\right)+3.4\left(5-2\right)+...+2015.2016\left(2017-2014\right)\)

\(\Rightarrow3A+6093360=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+2015.2016.2017-2014.2015.2016\)

\(\Rightarrow3A+6093360=2015.2016.2017\)

\(\Rightarrow3A+6093360=8183538080\)

\(\Rightarrow3A=8177444720\)

\(\Rightarrow A=2725814907\)

2410 là 24¹⁰

b: \(\left(-0,25\right)^3:\left(-0,25\right)=\left(-0,25\right)^{3-1}=\left(-0,25\right)^2=\left(-\frac14\right)^2=\frac{1}{16}\)

c: \(\left\lbrack\left(-0,5\right)^2\right\rbrack^2=\left\lbrack\left(\frac12\right)^2\right\rbrack^2=\left(\frac12\right)^4=\frac{1}{16}\)

d: \(a^5\cdot a^2=a^{5+2}=a^7\)

f: \(\frac{3^2}{\left(0,375\right)^2}=\left(\frac{3}{0,375}\right)^2=8^2=64\)

e: \(\left(\frac15\right)^5\cdot5^5=\left(\frac15\cdot5\right)^5=1^5=1\)

g: \(\frac{120^3}{40^3}=\left(\frac{120}{40}\right)^3=3^3=27\)

h: \(\left(0,125\right)^3\cdot512=\left(\frac18\right)^3\cdot8^3=1\)

(-5x²y + 3xy² + 7) + (-6x²y + 4xy² - 5)

= -5x²y + 3xy² + 7 - 6x²y + 4xy² - 5

= -11x²y + 7xy² + 2

(2,4x³ - 10x²y) + (7x²y - 2,4x³ + 3xy²)

= 2,4x³ - 10x²y + 7x²y - 2,4x³ + 3xy²

= -3x²y + 3xy²

Mình sửa lại câu cuối:

(15x²y - 7xy² - 6y²) + (2x² - 12x²y + 7xy²)

= 15x²y - 7xy² - 6y² + 2x² - 12x²y + 7xy²

= 3x²y - 6y² + 2x²

Chúc bn học tốt!

a, 2^4-x=32=2⁵

=> 4-x=5

<=> x=-1

b, (x+1,5)²+(y-2,5)¹⁰=0

Vì (x+1,5)2\(\ge\)0,   (y-2,5)¹⁰\(\ge\)0

\(\Rightarrow\hept{\begin{cases}x+1,5=0\\y-2,5=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=-1,5\\y=2,5\end{cases}}}\)

a)\(2^{4-x}\)=32

=>\(2^{4-x}\)=32=\(2^5\)

=>4-x=5

=>x=4-5=-1

=>x=-1

help me, please

Ta có: 12 + 22 + 32 + … + 102 = 385

A = 1002 + 2002 + 3002 + … + 10002

= (100.1)2 + (100.2)2 + (100.3)2 + … + (100.10)2

= 1002(12 + 22 + 32 + … + 102)

= 10000 . 385 = 3850000

bt làm rồi còn hỏi làm j