1)Tính:

a)\(4^2\cdot2=\left(2^2\right)^2\cdot2=2^4\cdot2=2^5=32\)

b)\(36^2:6^2=\left(36:6\right)^2=6^2=48\)

c)\(\left(\frac{2}{5}\right)^{10}:\left(\frac{4}{25}\right)^2=\left(\frac{2}{5}\right)^{10}\cdot\left(\frac{25}{4}\right)^2=\)\(\left(1\right)^{10}\cdot\left(\frac{5}{2}\right)^2=1\cdot\frac{5^2}{2^2}=1\cdot\frac{25}{4}=\frac{25}{4}\)

a

\(4^2.2=16.2=32\)

b\(36^2:6^2=36.36:6.6=36.36:36=36\)

c

3)

a)\(x:\left(-\frac{1}{3}\right)^5=\left(-\frac{1}{3}\right)^3\)

                      \(x=\left(-\frac{1}{3}\right)^3\cdot\left(-\frac{1}{3}\right)^5\)           

                      \(x=\left(-\frac{1}{3}\right)^8\)

b)\(\left(\frac{2}{3}\right)^{16}\cdot x=\left(\frac{2}{3}\right)^{18}\)

                      \(x=\left(\frac{2}{3}\right)^{18}:\left(\frac{2}{3}\right)^{16}\)

                      \(x=\left(\frac{2}{3}\right)^2\)

                      \(x=\frac{2^2}{3^2}\)

                      \(x=\frac{4}{9}\)

5.2²+(x+3)=5²

5.4+(x+3)=25

20+(x+3)=25

x+3=25-20

x-3=5

x=5+3

x=8

\(x=8\)

Trả lời

\(5.2^2+\left(x+3\right)=5^2\)

\(5.4+\left(x+3\right)=25\)

\(20+\left(x+3\right)=25\)

          \(x+3=25-20\)

          \(x+3=5\)

          \(x\)        \(=\) \(5-3\)

          \(x\)        \(=\) \(8\)

5 x 2^2 + 9 x ( X + 3 ) = 5^2

5 x 4 + 9 nhân ( X + 3 ) =25

20 +  9 ( x + 3 ) = 25

9( x + 3) = 5

x + 3 = 5 / 9

x = -4 / 9

a, 2¹.5².17 = 2.25.17 = 50.17 = 850 

b, 2² + 2³ + 2⁴ = 4 + 8 + 16 = 28

c, 2⁵.3 + 2⁴:8 + 50: 5²

= 32.3 + 16:8 + 50:25

=96 + 2 + 2

= 100

d, 11² - 10² - 3²

= 121 - 100 - 9

= 21 - 9

= 12

e, 1³ + 2³ + 3³ + 4³ + 5³

= ( 1+ 2+3+4+5)²

= 15²

= 225

\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}=\frac{1}{2.2}+\frac{1}{3.3}+\frac{1}{4.4}+...+\frac{1}{100.100}\)

\(< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{99.100}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

\(=1-\frac{1}{100}< 1\)(ĐPCM)

a)(1000+1):11

=1001:11

=91

91=7.13

b)14²+5²+2²

=196+25+4

=221+4

=225

225=3².5²

c)333:3+225:15²

=333:3+225:225

=111+1

=112

112=2⁴.7

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