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a, =\(\left(\dfrac{-1}{2}\times3\right)^7\) = (-1,5)\(^7\) = \(-17\dfrac{11}{128}\)
b,=(0,125)\(^3\) \(\times\) 8\(^3\) = ( 0,125\(\times\)8)\(^3\) =1\(^3\)=1
c,\(\dfrac{90^2}{15^2}\) = \(\left(\dfrac{90}{15}\right)^2\) =6\(^2\) =36
a) (1 / 7.7) 7 = 1
b) (0,125.8)3=1
c)( 0,25.0,25.32)2=22=4
d) (90/15) 3 = 6 3
) ( 790/79)4=104
f) (3/0,75)2=82
\(\left(\dfrac{1}{7}\right)^7\cdot7^7=\left(\dfrac{1}{7}\cdot7\right)^7=1^7=1\\ \left(0,125\right)^3\cdot512=\left(0,125\right)^3\cdot8^3=\left(0,125\cdot8\right)^3=1^3=1\\ \left(0,25\right)^4\cdot1024=\left(0,25\right)^4\cdot256\cdot4=\left(0,25\right)^4\cdot4^4\cdot4=\left(0,25\cdot4\right)^4\cdot4=1^4\cdot4=4\)
a) \(\left(\dfrac{1}{7}\right)^7.7^7=\left(\dfrac{1}{7}.7\right)^7=1^7=1\)
b) \(\left(0.125\right)^3.512=\left(0.125\right)^3.8^3=\left(0.125\cdot8\right)^3=1^3=1\)
c) \(\left(0.25\right)^4.1024=\left(0.25\right)^4.4^5=\left(0.25\right)^4.4^4.4=\left(0.25.4\right)^4.4=1^4.4=1.4=4\)
A) (1/5)^5 . 5^5 = 1/5^5 . 5^5 = 5^5 / 5^5 = 1.
B)(0,125)^3 . 512 = (1/8)^3 . 512 = 1/8^3 . 512 = 1/512 . 512 = 1.
C) (0,25)^4 . 1024 = (1/4)^4 . 1024 = 1/4^4 . 1024 = 1/256 . 1024 = 4.
\(\frac{625}{5^n}=5^3\)
\(\Leftrightarrow5^3\cdot5^n=625\)
\(\Leftrightarrow5^{3+n}=625\)
\(\Leftrightarrow5^{3+n}=5^4\)
\(\Leftrightarrow3+n=4\Leftrightarrow n=1\)
\(32< 2^x< 512\)
\(\Leftrightarrow2^5< 2^x< 2^9\)
\(\Leftrightarrow5< x< 9\)
\(\Leftrightarrow x\in\left\{6;7;8\right\}\)
a) \(\left(\dfrac{1}{2}\right)^3.\left(\dfrac{1}{4}\right)^2\)
\(=\dfrac{1}{8}.\dfrac{1}{16}\)
\(=\dfrac{1}{128}\)
b) \(16:\left(0,125\right)^3.512\)
\(=16:\dfrac{1}{512}.512\)
\(=16:\left(\dfrac{1}{512}.512\right)\)
\(=16:1\)
\(=16\)
a, \(\left(\dfrac{1}{2}\right)^3\). \(\left(\dfrac{1}{4}\right)^2\)
=\(\dfrac{1}{8}\).\(\dfrac{1}{16}\)
=\(\dfrac{1}{128}\)
b, 16 : (0,125)3.512
= 16 : \(\dfrac{1}{512}\).512
= 16 : 1
=16