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a) \(\left(\dfrac{2}{3}\right)^0\cdot\left(\dfrac{2}{3}\right)^5=1\cdot\left(\dfrac{2}{3}\right)^5=\left(\dfrac{2}{3}\right)^5\)
b) \(\left(\dfrac{6}{18}\right)^2:\left(\dfrac{7}{3}\right)^2=\left(\dfrac{6}{18}:\dfrac{7}{3}\right)^2=\left(\dfrac{1}{7}\right)^2\)
c) \(3^2\cdot2^5\cdot\left(\dfrac{2}{3}\right)^2=\left(3\cdot\dfrac{2}{3}\right)^2\cdot2^5=2^2\cdot2^5=2^{2+5}=2^7\)
d) \(\dfrac{50^3}{125}=\dfrac{50^3}{5^3}=\left(\dfrac{50}{5}\right)^3=10^3\)
`@` `\text {Ans}`
`\downarrow`
`b,`
\(\left(\dfrac{8}{3}\right)^8\cdot\left(\dfrac{9}{4}\right)^8\)
`= (8/3 * 9/4)^8`
`= 6^8`
`b(2),`
\(\left(\dfrac{6}{18}\right)^2\div\left(\dfrac{7}{3}\right)^2\)
`= (6/18 \div 7/3)^2`
`= (6/18 * 3/7)^2`
`= (1/7)^2`
`= 1/49`
`b(3),`
\(\left(\dfrac{6}{7}\right)^{13}\cdot\left(\dfrac{49}{18}\right)^{13}\)
`= (6/7 * 49/18)^13`
`= (7/3)^13`
`b(4),`
\(\left(-\dfrac{7}{15}\right)^3\div\left(\dfrac{21}{25}\right)^3\)
`= (-7/15 \div 21/25)^3`
`= (-7/15 * 25/21)^3`
`= (-5/9)^3`
`= (-125)/729`
`b(5),`
\(\left(-\dfrac{4}{13}\right)^5\div\left(\dfrac{26}{5}\right)^5\)
`= (-4/13 \div 26/5)^5`
`= (-4/13 * 5/26)^5`
`= (-10/169)^5`
`b(6),`
\(\left(-\dfrac{1}{4}\right)^{12}\cdot\left(\dfrac{12}{13}\right)^{12}\)
`= (-1/4 * 12/13)^12`
`= (-3/13)^12`
`@` `\text {Kaizuu lv uuu}`
