a) \(\left(\dfrac{1}{5}\right)^5.5^5=1\)

b) \(\left(0,125\right)^3.512=1\)

c) \(\left(0,25\right)^4.1024=4\)

a) (1/5)^5 . 5^5 = (1/5. 5)^5 = 1^5= 1

b) (0,125)^3. 512= (0,125)^3 . 8^3 = (0,125. 8)^3 = 1^3= 1

c) (0,25)^4. 1024= [(0,25)^2]^2. 32^2= (1/6)^2. 32^2=(1/6.32)^2= (32/6)^2 =2^2= 4

a, \(\left(\dfrac{1}{5}\right)^5.5^5\) =0,00032. 3125= 1

b, \(\left(0,125\right)^3.512\)= 0.001953125. 512=1

c, \(\left(0,25\right)^4.1024\) =0,00390625.1024=4

a/ \(\left(\dfrac{1}{5}\right)^5.5^5=\left(\dfrac{1}{5}.5\right)^5=1^5=1\)

b/ \(\left(0,125\right)^3.512=\left(0,125\right).8^3=\left(0,125.8\right)^3=1^3=1\)

c/ \(\left(0,25\right)^4.1024=\left(0,25^2\right)^2.32^2=\left(\dfrac{1}{6}\right)^2.32^2=\left(\dfrac{1}{6}.32\right)^2=16^2\)

\(a,\left(\dfrac{1}{5}\right)^5.5^5=\left(\dfrac{1}{5}.5\right)^5=1^5=1\)

\(b,\left(0,125\right)^3.512=\left(0,125\right)^3.8^3=\left(0,125.8\right)^3=1^3=1\)

\(c,\left(0,25\right)^4.1024=\left(0,25\right)^4.4^4.4=\left(0,25.4\right)^4.4=1^4.4=1.4=4\)

a) \(\left(\dfrac{1}{5}\right)^5.5^5\)

\(=\dfrac{1}{3125}.3125\)

= 1

b) \(\left(0,125\right)^3.512\)

\(=\dfrac{1}{512}.512\)

= 1

c) \(\left(0,25\right)^4.1024\)

= \(\dfrac{1}{256}.1024\)

= 4

50.

a) \(\left(\dfrac{1}{5}\right)^5.5^5\)

\(=\left(5^{-1}\right)^5.5^5=5^{-5}.5^5=5^{-5+5}=5^0=1\)

\(a,\left(\dfrac{1}{7}\right)^7.7^7=\left(\dfrac{1}{7}.7\right)^7=1\)

\(b,\left(0,125\right)^3.512=\left(0,125\right)^3.8^3=\left(0,125.8\right)^3=1^3=1\)\(c,\left(0,25\right)^4.1024=\left(\left(0,25\right)^2\right)^2.32^2=\left(\dfrac{1}{6}\right)^2.32^2=\left(\dfrac{1}{6}.32\right)^2=2^2=4\)

\(d,\dfrac{90^3}{15^3}=\left(\dfrac{90}{15}\right)^3=6^3=216\)

\(a,25^3:5^2=5^{2^3}:5^2=5^6:5^2=5^4=625\)

\(b,\frac{390^4}{130^4}=\left(\frac{390}{130}\right)^4=3^4=81\)

\(c,32^4:4^3=2^{5^4}:2^{2^3}=2^{20}:2^6=2^{14}\)

a) \({\left( {\frac{8}{9}} \right)^3} \cdot \frac{4}{3} \cdot \frac{2}{3} = {\left( {\frac{8}{9}} \right)^3}.\frac{8}{9} = {\left( {\frac{8}{9}} \right)^{3+1}}={\left( {\frac{8}{9}} \right)^4}\)

b) \({\left( {\frac{1}{4}} \right)^7} \cdot 0,25 = {\left( {0,25} \right)^7}.0,25 ={\left( {0,25} \right)^{7+1}}= {\left( {0,25} \right)^8}\)

c) \({( - 0,125)^6}:\frac{{ - 1}}{8} = {\left( {\frac{{ - 1}}{8}} \right)^6}:\frac{{ - 1}}{8} = {\left( {\frac{{ - 1}}{8}} \right)^{6-1}}= {\left( {\frac{{ - 1}}{8}} \right)^5}\)

d) \({\left[ {{{\left( {\frac{{ - 3}}{2}} \right)}^3}} \right]^2} = {\left( {\frac{{ - 3}}{2}} \right)^{3.2}} = {\left( {\frac{{ - 3}}{2}} \right)^6}\)

a) \(\left(\frac{3}{7}\right)^{21}:\left(\frac{3}{7}^3\right)^6\)

\(=\left(\frac{3}{7}\right)^{21}:\left(\frac{3}{7}\right)^{18}\)

\(=\left(\frac{3}{7}\right)^{21-18}\)

\(=\left(\frac{3}{7}\right)^3\)

\(=\frac{27}{343}\)

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