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a) \(8^{15}.4^{13}=\left(2^3\right)^{15}.\left(2^2\right)^{13}=2^{45}.2^{26}=2^{71}\)
b) \(\left(\frac{1}{2}\right)^{18}.\left(\frac{1}{4}\right)^{28}=\left(\frac{1}{2}\right)^{18}.\left(\frac{1}{2^2}\right)^{28}=\frac{1}{2^{18}}.\frac{1}{2^{56}}=\frac{1}{2^{74}}=\left(\frac{1}{2}\right)^{74}\)
c) \(9^{12}.27^{10}=\left(3^2\right)^{12}.\left(3^3\right)^{10}=3^{24}.3^{30}=3^{54}\)
a) = (23)15. (22)13 = 245.226 = 271
b) = \(\left(\frac{1}{2}\right)^{18}.\left(\left(\frac{1}{2}\right)^2\right)^{28}=\left(\frac{1}{2}\right)^{18}.\left(\frac{1}{2}\right)^{56}=\left(\frac{1}{2}\right)^{18+56}=\left(\frac{1}{2}\right)^{74}\)
c) = (32)12.(33)10 = 324.330 = 324+30 = 354
\(a,9.3^3.\frac{1}{81}.3^2=3^2.3^3.3^{\left(-4\right)}.3^2=3^{2+3-4+2}=3^3.\)
\(b,4.2^5:\left(2^3.\frac{1}{16}\right)=2^2.2^5:\left(2^3.2^{-4}\right)=2^{2+5}:2^{3-4}=2^7:2^{-1}=2^{7-\left(-1\right)}=2^8.\)
\(c,3^2.2^5.\left(\frac{2}{3}\right)^2=3^2.2^5.\frac{2^2}{3^2}=\left(\frac{3^2}{3^2}\right).\left(2^5.2^2\right)=1.2^{5+2}=2^7\)
\(d,\left(\frac{1}{3}\right)^2.\frac{1}{3}.9^2=\left(\frac{1}{3}\right)^2.\frac{1}{3}.\left(3^2\right)^2=\left(\frac{1}{3}\right)^{2+1}.3^4=\left(\frac{1}{3}\right)^3.\left(\frac{1}{3}\right)^{-4}=\left(\frac{1}{3}\right)^{3-4}=\left(\frac{1}{3}\right)^{-1}=3^1\)
a: \(1=4^0\)
\(4=4^1\)
\(16=4^2\)
\(256=4^4\)
b: \(\dfrac{1}{4}=4^{-1}\)
\(\dfrac{1}{64}=4^{-3}\)
\(\dfrac{1}{256}=4^{-4}\)
\(\dfrac{1}{16}=4^{-2}\)
\(\dfrac{1}{1024}=4^{-5}\)