`@` `\text {Ans}`
`\downarrow`
`4,`
`a)`
`(4/9+1/3)^2`
`= (7/9)^2`
`= 49/81`
`b)`
`(1/2-3/5)^3`
`= (-1/10)^3`
`= -1/1000`
`c)`
`(1/3)^3*4 + 3/4`
`= 1/27*4 + 3/4`
`= 4/27 + 3/4`
`= 97/108`
`d)`
`7 - (-4/5)^0 + (1/3)^2 \div 2`
`= 7 - 1 + 1/9 \div 2`
`= 6 + 1/18`
`= 109/18`
`e)`
`4^3 \div 2^5 + 3^5 \div 9^2`
`= (2^2)^3 \div 2^5 + 3^5 \div (3^2)^2`
`= 2^6 \div 2^5 + 3^5 \div 3^4`
`= 2 + 3`
`= 5`
`g)`
`9*3^7 \div (3^10*1/27)`
`= 3^2*3^7 \div (3^7)`
`= 3^2 * 3^7 \div 3^7`
`= 3^2=9`
a) \(\left(\dfrac{4}{9}+\dfrac{1}{3}\right)^2\)
\(=\left(\dfrac{4}{9}+\dfrac{3}{9}\right)^2\)
\(=\left(\dfrac{7}{9}\right)^2\)
\(=\dfrac{7^2}{9^2}\)
\(=\dfrac{49}{81}\)
b) \(\left(\dfrac{1}{2}-\dfrac{3}{5}\right)^3\)
\(=\left(\dfrac{5}{10}-\dfrac{6}{10}\right)^3\)
\(=\left(-\dfrac{1}{10}\right)^3\)
\(=-\dfrac{1^3}{10^3}\)
\(=-\dfrac{1}{1000}\)
c) \(\left(\dfrac{1}{3}\right)^3\cdot4+\dfrac{3}{4}\)
\(=\dfrac{1}{27}\cdot4+\dfrac{3}{4}\)
\(=\dfrac{4}{27}+\dfrac{3}{4}\)
\(=\dfrac{97}{108}\)
d) \(7-\left(-\dfrac{4}{5}\right)^0+\left(\dfrac{1}{3}\right)^2:2\)
\(=7-1+\dfrac{1}{9}:2\)
\(=6+\dfrac{1}{18}\)
\(=\dfrac{109}{18}\)
e) \(4^3:2^5+3^5:9^2\)
\(=\left(2^2\right)^3:2^5+3^5:\left(3^2\right)^2\)
\(=2^6:2^5+3^5:3^4\)
\(=2^1+3^1\)
\(=5\)
f) \(9\cdot3^7:\left(3^{10}\cdot\dfrac{1}{27}\right)\)
\(=3^2\cdot3^7:\left(3^{10}\cdot\dfrac{1}{3^3}\right)\)
\(=3^9:\left(\dfrac{3^{10}}{3^3}\right)\)
\(=3^9:3^7\)
\(=3^2\)
\(=9\)
