Bài 4:
a: \(2^3\cdot2^5=2^{3+5}=2^8\)
\(\left(-3\right)^9:\left(-3\right)^5=\left(-3\right)^{9-5}=\left(-3\right)^4\)
\(\left(-6\right)^9\cdot6^5=-6^9\cdot6^5=-6^{14}\)
\(\left(\frac12\right)^5=\frac{1^5}{2^5}=\frac{1}{32}\)
b: \(\left(\frac35\right)^6\cdot\left(\frac53\right)^6=\left(\frac35\cdot\frac53\right)^6=1^6=1\)
\(\left(-\frac78\right)^9:\left(\frac74\right)^9=\left(-\frac78:\frac74\right)^9=\left(-\frac48\right)^9=\left(-\frac12\right)^9\)
\(\left\lbrack\left(-\frac12\right)^2\right\rbrack^3=\left\lbrack\left(\frac12\right)^2\right\rbrack^3=\left(\frac12\right)^{2\cdot3}=\left(\frac12\right)^6\)
c: \(\left(\frac23\right)^8=\left\lbrack\left(\frac23\right)^4\right\rbrack^2\)
\(\left(\frac13\right)^{12}:\left(-\frac39\right)^{12}=\left(\frac13\right)^{12}:\left(-\frac13\right)^{12}=1\)
\(\left(\frac13\right)^{12}:\left(\frac13\right)^{10}=\left(\frac13\right)^{12-10}=\left(\frac13\right)^2=\frac19\)
Bài 5:
a: \(\frac{\left(-5\right)^{60}\cdot3^{50}}{15^5\cdot5^{61}}=\frac{5^{60}\cdot3^{50}}{3^5\cdot5^5\cdot5^{61}}=\frac{3^{45}}{5^6}\)
b: \(\left(-\frac13\right)^2-\left(-\frac{12}{17}\right)^0+\left(-\frac12\right)^3\cdot4^2\)
\(=\frac19-1+\frac{-1}{8}\cdot16=\frac19-1-2=\frac19-3=-\frac{26}{9}\)
c: \(\frac{\left(-3\right)^{10}\cdot15^5}{25^3\cdot\left(-9\right)^7}=\frac{3^{10}\cdot3^5\cdot5^5}{-3^{14}\cdot5^6}=\frac{3^{15}}{3^{14}}\cdot\frac{-1}{5}=\frac{-3}{5}\)
d: \(2^3+3\cdot\left(\frac13\right)^0-2^{-2}\cdot4+\left\lbrack\left(-2\right)^2:\frac12\right\rbrack\cdot8=8+3-1+8\cdot8\)
=11-1+64
=10+64
=74
