A) 4¹⁰ . 8¹⁵ = (2²)¹⁰ . (2³)¹⁵ = 2²⁰ . 2⁴⁵ = 2²⁰⁺⁴⁵=2⁶⁵

B) 4¹⁵ . 5³⁰ = (2²)¹⁵ . 5³⁰ = 2³⁰ . 5³⁰ = (2 . 5)³⁰ = 10³⁰

C) 27¹⁶ : 9¹⁰ = (3³)¹⁶ : (3²)¹⁰ = 3⁴⁸ : 3²⁰ =  3^48-20=3²⁸

20²-15².3[5²+22+2022⁰

a: \(\dfrac{-35}{-7}=\dfrac{35}{7}=5\)

b: \(\dfrac{42}{-21}=-\dfrac{42}{21}=-2\)

c: \(\dfrac{55}{-5}=-\dfrac{55}{5}=-11\)

d: \(\dfrac{46}{-23}=-\dfrac{46}{23}=-2\)

e: \(-30:\left(-2\right)=\dfrac{30}{2}=15\)

f: \(23\cdot\left(-4\right)=-23\cdot4=-92\)

g: \(15\cdot\left(-3\right)\cdot0=15\cdot0=0\)

h: \(-32\cdot14=-32\cdot10-32\cdot4=-320-128=-448\)

\(\sqrt{15-6\sqrt{6}}+\sqrt{35-12\sqrt{6}}=\sqrt{\left(3-\sqrt{6}\right)^2}+\sqrt{\left(3\sqrt{3}-2\sqrt{2}\right)^2}\)

\(=3-\sqrt{6}+3\sqrt{3}-2\sqrt{2}\)

\(\sqrt{17-3\sqrt{32}}+\sqrt{17+3\sqrt{32}}=\sqrt{\left(3-2\sqrt{2}\right)^2}+\sqrt{\left(3+2\sqrt{2}\right)^2}\)

\(=3-2\sqrt{2}+3+2\sqrt{2}=6\)

\(\sqrt{49-5\sqrt{96}}+\sqrt{49+5\sqrt{96}}=\sqrt{\left(5-2\sqrt{6}\right)^2}+\sqrt{\left(5+2\sqrt{6}\right)^2}\)

\(=5-2\sqrt{6}+5+2\sqrt{6}=10\)

\(\sqrt{13-\sqrt{160}}+\sqrt{53+4\sqrt{90}}=\sqrt{\left(2\sqrt{2}-\sqrt{5}\right)^2}+\sqrt{\left(3\sqrt{5}+2\sqrt{2}\right)^2}\)

\(=2\sqrt{2}-\sqrt{5}+3\sqrt{5}+2\sqrt{2}=2\sqrt{5}+4\sqrt{2}\)

a: \(\sqrt{15-6\sqrt{6}}+\sqrt{35-12\sqrt{6}}\)

\(=3-\sqrt{6}+3\sqrt{3}-2\sqrt{2}\)

b: \(\sqrt{17-3\sqrt{32}}+\sqrt{17+3\sqrt{32}}\)

\(=3-2\sqrt{2}+3+2\sqrt{2}\)

=6

c: Ta có: \(\sqrt{49-5\sqrt{96}}+\sqrt{49+5\sqrt{96}}\)

\(=5-2\sqrt{6}+5+2\sqrt{6}\)

=10

d: Ta có: \(\sqrt{13-\sqrt{160}}+\sqrt{53+4\sqrt{90}}\)

\(=\sqrt{13-4\sqrt{10}}+\sqrt{53+4\sqrt{90}}\)

\(=2\sqrt{2}-\sqrt{5}+3\sqrt{5}+2\sqrt{2}\)

\(=2\sqrt{5}+4\sqrt{2}\)

Bài 2: 

a: A=(12,87+14,13)+(-14,7-37,3)

=27-52=-25

b: B=-1/3+2/5-2/3-3/5+1/5

=-1

mn ơi e vít nhầm là tính rồi rút gọn mn sửa lại là rút gọn rùi tính

a: =-12/20+5/20-6/20

=-13/20

b: =10/50-45/50-14/50

=-49/50

c: =31/23-7/32-8/23=1-7/32=25/32

`a)-3/5 + 1/4 + -3/10= (-12)/20 + 5/20 + (-6)/20 = -13/20` 

`b)1/5 + -9/10 + (-7/25)= 10/50 + (-45)/50 + (-14)/50 = (-49)/50`

`c)31/23 - ( 7/32 + 8/23 )=  31/23 - 417/736 =992/736 - 417/736  =  575/736=25/32  `

a) bé hệ số lại

A/3=a^2+9b^2+5/3.c^2-6ab-10c+79

=(a-3b)^2+5/3(c^2-2.3/2.c+9/4)+79-5/3.9/4

=(a-3b)^2+5/3(c-3/2)^2+79-15/4

Amin =3.(79-15/4)

đẳng thức khi a=3b và c=3/2

Kiểm tra số liệu cộng trừ nhân chia

\(ax+\frac{b}{\left(x^2-4\right)}-\frac{1}{\left(x-2\right)}=\frac{2}{x}+2\) đúng vậy ko

Kiểu gì cũng được nhưng nếu không đúng => lạc đề

Lần sau gặp pHân số dùng f(x) viết đi

tách ra đi 

Dài quá :(

a) \(1-\dfrac{1}{2}+\dfrac{1}{3}=\dfrac{6}{6}-\dfrac{3}{6}+\dfrac{2}{6}=\dfrac{6-3+2}{6}=\dfrac{1}{6}\)

\(b.\) \(\dfrac{2}{5}+\dfrac{3}{5}:\dfrac{9}{10}=\dfrac{2}{5}+\dfrac{3}{5}.\dfrac{10}{9}=\dfrac{2}{5}+\dfrac{2}{3}=\dfrac{6}{15}+\dfrac{10}{15}=\dfrac{6+10}{15}=\dfrac{16}{15}\)

\(c.\) \(\dfrac{7}{11}.\dfrac{3}{4}+\dfrac{7}{11}.\dfrac{1}{4}+\dfrac{4}{11}=\dfrac{21}{44}+\dfrac{7}{44}+\dfrac{4}{11}=\dfrac{21}{44}+\dfrac{7}{44}+\dfrac{16}{44}=\dfrac{21+7+16}{44}=\dfrac{44}{44}=1\)

a/\(1-\dfrac{1}{2}+\dfrac{1}{3}=\dfrac{6}{6}-\dfrac{3}{6}+\dfrac{2}{6}=\dfrac{5}{6}\)

b/\(\dfrac{2}{5}+\dfrac{3}{5}:\dfrac{9}{10}=\dfrac{2}{5}+\dfrac{3}{5}.\dfrac{10}{9}=\dfrac{2}{5}+\dfrac{2}{3}=\dfrac{6}{15}+\dfrac{10}{15}=\dfrac{16}{15}\)