a.
\(\left(0,25\right)^3\times32\)
\(=\left(0,25\right)^3\times2^5\)
\(=\left(0,25\right)^3\times2^3\times2^2\)
\(=\left(0,25\times2\right)^3\times4\)
\(=\left(0,5\right)^3\times4\)
\(=0,125\times4\)
\(=0,5\)
b.
\(\left(-0,125\right)^3\times80^4\)
\(=\left(-0,125\right)^3\times80^3\times80\)
\(=\left(-0,125\times80\right)^3\times80\)
\(=\left(-10\right)^3\times80\)
\(=-1000\times80\)
\(=-80000\)
c.
\(3^{1994}+3^{1993}-3^{1992}\)
\(=3^{1992}\times\left(3^2+3-1\right)\)
\(=3^{1992}\times\left(9+3-1\right)\)
\(=3^{1992}\times11\)
\(\Rightarrow3^{1994}+3^{1993}-3^{1992}⋮11\)
d.
\(4^{13}+32^5-8^8\)
\(=\left(2^2\right)^{13}+\left(2^5\right)^5-\left(2^3\right)^8\)
\(=2^{26}+2^{25}-2^{24}\)
\(=2^{24}\times\left(2^2+2-1\right)\)
\(=2^{24}\times\left(4+2-1\right)\)
\(=2^{24}\times5\)
\(\Rightarrow4^{13}+32^5-8^8⋮5\)
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