4^5*32^{10}=(2^2)^5*(2^5)^{10}=2^{10}*2^{50}=2^{10+50}=2^{60}
9*5^{99}-4*5^{99}=5^{99}(9-4)=5^{99}*5=5^{99+1}=5^{100}
- liczba 86^{5} · 216^{4} jest równa
(\sqrt2)^{-3}=(\frac{1}{\sqrt2})^3=\frac{1}{\sqrt{8}}=\frac{1}{2\sqrt2}=\frac{\sqrt2}{2\sqrt2*\sqrt2}=\frac{\sqrt2}{2*2}=\frac{\sqrt2}{4}
27^{-\frac{1}{3}}=(3^3)^{-\frac{1}{3}}=3^{3*(-\frac{1}{3})}=3^{-1}=\frac{1}{3}
\sqrt[3]7*\sqrt7=7^{\frac{1}{3}}*7^\frac{1}{2}=7^{\frac{2}{6}}+7^{\frac{3}{6}}=7^{\frac{5}{6}}=\sqrt[6]{7^5}
5^2*5^{-2}=5^{2+(-2)}=5^0=1
(\sqrt{55})^{55} : (\sqrt{11})^{55}=\frac{(\sqrt5)^{55}*(\sqrt{11})^{55}}{(\sqrt{11})^{55}}=(\sqrt{5})^{55}
27^{15}*81^{25}*3=(3^3)^{15}*(3^4)^{25}*3=3^{45}*3^{100}*3=3^{45+100+1}=3^{146}