5mu13 : 5mu10 - 25*2mu2
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`@` `\text {Ans}`
`\downarrow`
`5^6 \div 5^3 + 2^2*2^3`
`= 5^3 + 2^5`
`= 125+32`
`=``157`
`19^7 \div 19^5 + 4*4^2`
`= 19^(7-5) + 4^(1+2)`
`= 19^2 + 4^3`
`= 361 + 64`
`=``425`
\(2^5\cdot7+3^{2019}\div3^{2018}?\)
`= 224 + 3`
`= 227`
`17*3^2 - 5^15 \div 5^13 + 39^0`
`= 153 - 5^2 + 1`
`= 153 - 125 + 1`
`= 153 - 124`
`=29`
\(S=\dfrac{2^2}{1.2}+\dfrac{2^2}{2.3}+\dfrac{2^2}{3.4}+...+\dfrac{2^2}{2022.2023}\)
\(S=2^2.\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{2022.2023}\right)\)
\(S=2^2.\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2022}-\dfrac{1}{2023}\right)\)
\(S=2^2.\left(\dfrac{1}{1}-\dfrac{1}{2023}\right)\)
\(S=2^2.\dfrac{2022}{2023}\)
\(S=\dfrac{2^2.2022}{2023}=\dfrac{8088}{2023}\)
S = 22 + 42 + 62 + ... + 202
= (2.1)2 + (2.2)2 + (2.3)2 ... (2.10)2
= 22.12 + 22.22 + 22.32 + ... + 22.102
= 22 (12 + 22 + ... + 102 )
= 4 . 385
= 1540
= (1x2)^2 (2x2)^2 (3x2)^2 (4x2)^2 ..... (9x2)^2 (10x2)^2
= 1^2 x 2^2 2^2 x 2^2 3^2 x 2^2 4^2 x 2^2 ..... 9^2 x 2^2 10^2 x 2^2
= (1^2 2^2 3^2 4^2 ..... 9^2 10^2) x 2^2
= 385 x 2^2 = 385 x 4 = 1540
a ) ( 13 - 145 + 49 ) - ( 13 + 49 )
= 13 - 145 + 49 - 13 - 49
= ( 13 - 13 ) - 145 + ( 49 - 49 )
= 0 - 145 + 0
= - 145
b) 25 . 22 . ( 15 - 18 ) + ( 12 - 19 + 10 )
= 25 . 4 . ( -3 ) + 7
= 100 . [ ( -3 ) + 7 ]
= 100 . 4
= 400
a ) ( 13 - 145 + 49 ) - ( 13 + 49 )
= 13 - 145 + 49 - 13 - 49
= ( 13 - 13 ) - 145 + ( 49 - 49 )
= 0 - 145 + 0
= - 145
\(4^2\cdot56-16:2^2\)
\(=16\cdot56-2^4:2^2\)
\(=896-2^2\)
\(=892\)
513 : 510 - 25 * 22
= 513-10 - 25 * 4
= 53 - 100
= 125 - 100
= 25