a: \(\left(-2\right)^2\cdot\left(-2\right)^3=\left(-2\right)^{2+3}=\left(-2\right)^5=-32\)
b: \(a^5\cdot a^7=a^{5+7}=a^{12}\)
c: \(\dfrac{9}{5}\cdot\left(1,8\right)^5=\dfrac{9}{5}\cdot\left(\dfrac{9}{5}\right)^5=\left(\dfrac{9}{5}\right)^6\)
d: \(\left(-\dfrac{3}{2}\right)^7:\dfrac{9}{4}=\left(-\dfrac{3}{2}\right)^7:\left(-\dfrac{3}{2}\right)^2\)
\(=\left(-\dfrac{3}{2}\right)^5=\dfrac{\left(-3\right)^5}{2^5}=-\dfrac{243}{32}\)
e: \(\left(-\dfrac{1}{3}\right)^6:\left(\dfrac{1}{6}\right)^2\)
\(=\dfrac{1}{3^6}:\dfrac{1}{6^2}\)
\(=\dfrac{1}{3^6}\cdot\dfrac{6^2}{1}=\dfrac{3^2\cdot2^2}{3^6}=\dfrac{2^2}{3^4}=\dfrac{4}{81}\)
`a, (-2)^2 . (-2)^3`
`= (-2)^(2 + 3)`
`= (-2)^5 = -32`
`b, a^5 * a^7`
`= a^(5 + 7)`
`= a^12`
`c, 9/5 * (1,8)^5`
`= (1,8)^1 * (1,8)^5`
`= (1,8)^(1 + 5)`
`= (1,8)^6`
`d, (-3/2)^7 : 9/4`
`= (-3/2)^7 : (-3/2)^2`
`= (-3/2)^5`
`= -243/32`
`e, (-1/3)^6 : (1/6)^2`
`= 1/(3^6) : 1/(6^2)`
`= (3^2 . 2^2)/(3^6) `
`= 4/81`
\(a,\left(-2\right)^2.\left(-2\right)^3\)
\(=\left(-2\right)^{2+3}\)
\(=\left(-2\right)^5\)
\(=-32\)
\(b,a^5.a^7=a^{5+7}=a^{12}\)
\(c,\dfrac{9}{5}.\left(1,8\right)^5=\dfrac{9}{5}.\left(\dfrac{9}{5}\right)^5=\left(\dfrac{9}{5}\right)^{1+5}=\left(\dfrac{9}{5}\right)^6\)
\(d,\left(\dfrac{-3}{2}\right)^7:\dfrac{9}{4}\)
\(=\left(-\dfrac{3}{2}\right)^7:\left(-\dfrac{3}{2}\right)^2\)
\(=\left(\dfrac{-3}{2}\right)^{7-2}\)
\(=\left(\dfrac{-3}{2}\right)^5\)
\(e,\left(\dfrac{-1}{3}\right)^6:\left(\dfrac{1}{6}\right)^2\)
\(=\dfrac{1}{3^6}.\dfrac{6^2}{1}\)
\(=\dfrac{6^2}{3^6}\)
\(=\dfrac{\left(3.2\right)^2}{3^6}\)
\(=\dfrac{3^2.2^2}{3^6}=\dfrac{1.2^2}{3^4}=\dfrac{4}{81}\)
