0, 125³ . 512 = 0, 125³ . 8³ = (0,125 .8 )³ =1³ = 1.

\(0,125^3.512\)

=\(\left(\dfrac{1}{8}\right)^3.8^3\)

= \(\dfrac{1}{8^3}.8^3\)

=\(6^3\)

  (0,125)³. 512

=  (0,125)³. 8³

= (0,125.8)³

= 1³

= \(\left(\dfrac{1}{1^{ }}\right)^3\)

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

\(1,\\ a,=\left(\dfrac{1}{4}\right)^3\cdot32=\dfrac{1}{64}\cdot32=\dfrac{1}{2}\\ b,=\left(\dfrac{1}{8}\right)^3\cdot512=\dfrac{1}{512}\cdot512=1\\ c,=\dfrac{2^6\cdot2^{10}}{2^{20}}=\dfrac{1}{2^4}=\dfrac{1}{16}\\ d,=\dfrac{3^{44}\cdot3^{17}}{3^{30}\cdot3^{30}}=3\\ 2,\\ a,A=\left|x-\dfrac{3}{4}\right|\ge0\\ A_{min}=0\Leftrightarrow x=\dfrac{3}{4}\\ b,B=1,5+\left|2-x\right|\ge1,5\\ A_{min}=1,5\Leftrightarrow x=2\\ c,A=\left|2x-\dfrac{1}{3}\right|+107\ge107\\ A_{min}=107\Leftrightarrow2x=\dfrac{1}{3}\Leftrightarrow x=\dfrac{1}{6}\)

\(d,M=5\left|1-4x\right|-1\ge-1\\ M_{min}=-1\Leftrightarrow4x=1\Leftrightarrow x=\dfrac{1}{4}\\ 3,\\ a,C=-\left|x-2\right|\le0\\ C_{max}=0\Leftrightarrow x=2\\ b,D=1-\left|2x-3\right|\le1\\ D_{max}=1\Leftrightarrow x=\dfrac{3}{2}\\ c,D=-\left|x+\dfrac{5}{2}\right|\le0\\ D_{max}=0\Leftrightarrow x=-\dfrac{5}{2}\)

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

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

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

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

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

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

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

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

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

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