Zadania w załączniku.... Question from @Havs

December 2018 1 15 Report

Zadania w załączniku

Mataszka 1)a) $3^{-x}$ =27
$3^{-x}$ = $3^{3}$
-x=3
x=-3
sprawdzenie:
$3^{-(-3)}$ =27
$3^{3}$ =27
27=27
b) $11^{3x-15}$ =1
$11^{3x-15}$ = $11^{0}$
3x-15=0
3x=15 /:3
x=5
c) $(1,5)^{2x+6}$ =5 $\frac{1}{16}$
$\frac{15}{10} ^{2x+6}$ = $\frac{81}{16}$
$\frac{3}{2} ^{2x+6}$ = $\frac{9}{4} ^{2}$
$\frac{3}{2} ^{2x+6}$ = $\frac{3}{2} ^{4}$
2x+6=4
2x=4-6
2x=-2 /:2
x=-1

2]a) $((xy)^{30}$ : $(xy)^{25}$ = $(xy)^{5}$
$((xy)^{30-25} )$ = $(xy)^{5}$
$(xy)^{5}$ = $( xy)^{5}$
b)( $a^{10}$ · $a^{7}$ )·( $b^{12-8}$ )²=
( $a^{6}$ · $a^{8}$ )²·( $b^{20-12}$ )²
( $a^{17}$ )²·( $b^{4}$ )²=( $a^{14}$ )²·( $b^{8}$ )²
$a^{34}$ · $b^{8}$ = $a^{28}$ · $b^{16}$
3a) $2^{-2}$ + $3^{3}$ = $\frac{1}{2} ^{2}$ +27= $\frac{1}{4}$ +27=27 $\frac{1}{4}$
b) $4^{-3} - 4^{-2}$ = $\frac{1}{4} ^{3} - \frac{1}{4} ^{2}$ = $\frac{1}{64} - \frac{1}{16} = \frac{1}{64} - \frac{4}{64} =- \frac{3}{64}$
c) $2^{1} + 3^{0} + 4^{1} + 5^{0} =2+1+4+1= 8$
d) $2^{-3} - 3^{-2} + 4^{-1} = \frac{1}{2} ^{3} - \frac{1}{3} ^{2} + \frac{1}{4} ^{1} = \frac{1}{8} - \frac{1}{9} + \frac{1}{4} = \frac{9}{72} - \frac{8}{72} + \frac{18}{72} = \frac{19}{72}$
e)·· $6^{-3}$ · $10^{2}$ · $6^{2}$ · $5^{-3}$ = $6^{-3}$ · $6^{2}$ ·(5·2)²· $5^{-3}$ = $6^{-3+2}$ · $5^{2}$ · $2^{2}$ · $5^{-3}$ = $6^{-1}$ · $5^{2+(-3)}$ · $2^{2}$ = $\frac{1}{6}$ · $5^{-1}$ ·4= $\frac{1}{6}$ · $\frac{1}{5}$ ·4= $\frac{2}{15}$
f) $\frac{5}{3} ^{-2}$ : $1 \frac{2}{3} ^{-1}$ · $(-0,125)^{0} = \frac{3}{5} ^{2}$ : $\frac{3}{5} ^{1}$ ·1= $\frac{3}{5} ^{2-1}$ = $\frac{3}{5}$
4)a) $5 \frac{1}{4} ^{-1}$ · $\frac{1}{7} ^{-1}$ -4· $\frac{1}{3} ^{-2}$ - $0,75^{-1}$ = $\frac{21}{4} ^{-1}$ ·7-4·3²- $\frac{75}{100} ^{-1}$ = $\frac{4}{21}$ ·7-4·9- $\frac{4}{3}$ = $\frac{4}{3} -36- \frac{4}{3} =-36$
b)7· $(0,6^{2} + \frac{5}{4} ^{-2} ) ^{-2}$ - $3^{-1}$ · $\frac{1}{3} ^{-2}$ ·2=7· $(0,36+ \frac{4}{5 } ^{2} ) ^{-2} - \frac{1}{3}$ ·3²·2=7· $(0,36+ \frac{16}{25} ) ^{-2}$ - $\frac{1}{3}$ ·9·2=7· $(0,36+0,64) ^{-2} -6=$ 7·1-6=7-6=1
5]2·4·3=24

2 votes Thanks 1