\(4^2\cdot120-4^3\cdot17+4^2\cdot34\)

\(=4^2\left(120-4\cdot17+34\right)\)

\(=16\left(120-68+34\right)\)

\(=16\cdot86=1088\)

\(7^3\cdot9+3^2\cdot7^4-45\cdot539\)

\(=7^3\cdot9+9\cdot7^4-45\cdot7^2\cdot11\)

\(=7^2\left(7\cdot9+9\cdot7^2-45\cdot11\right)\)

\(=49\left(63+9\cdot49-495\right)\)

\(=49\left(63+441-495\right)\)

\(=49\cdot9=441\)

\(5\cdot10^4+4\cdot10^3+6\cdot10^2+5\cdot10+9\)

\(=10\left(5\cdot10^3+4\cdot10^2+10\cdot6\right)+9\)

\(=10\left(5\cdot1000+4\cdot100+60\right)+9\)

\(=10\left(5000+400+60\right)+9\)

\(=10\cdot5460+9=54600+9=54609\)

Ta có: \(A=100^2+200^2+300^2+...+1000^2\)

\(=100^2\cdot\left(1+2^2+3^2+...+10^2\right)\)

\(=100^2\cdot385=3850000\)

3800

3850

\(\Leftrightarrow x-1=2\)

hay x=3

Ta có:

A=310.11+310.539.24=310.(11+5)39.16A=310.11+310.539.24=310.(11+5)39.16

=310.1639.16=3.11.1=3=310.1639.16=3.11.1=3

Vậy giá trị biểu thức A là 3

\(A=\frac{2}{3}+\frac{2}{3^2}+\frac{2}{3^3}+...+\frac{2}{3^{10}}=2\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{10}}\right)\)

\(=>3A=2\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^9}\right)\)

\(=>3A-A=2\left[\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^9}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{10}}\right)\right]\)

\(=>2A=2\left(1-\frac{1}{3^{10}}\right)=>A=1-\frac{1}{3^{10}}\)

A=5 296 163 666_x10¹⁵

P = 3² + 6² + 9² + ... + 30²

P = 3² . (1² + 2² + 3² + ... + 10²)

P = 9 . 385

P = 3465

a) C = 10⁶ + 5⁷

C = 2⁶ . 5⁶ + 5⁷

C = 5⁶ . (2⁶ + 5)

C = 5⁶ . (64 + 5)

C = 5⁶ . 69 chia hết cho 69

b) 3¹⁰ . 199 - 3⁹ . 500

= 3⁹ . (3.199 - 500)

= 3⁹ . (597 - 500)

= 3⁹ . 97 chia hết cho 97

\(2^3\)+ \(3^2\)+ \(5^1\) = 360

       Học tốt!

 \(2^3\cdot3^2\cdot5^1\)
=\(8\cdot9\cdot5\)
=\(360\)

2^3x 3^2 x 5^1

8x9x5

4500