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\(7^{25}:\left(7^{21}.46+7^{21}.3\right)\)
\(=7^{25}:\left[7^{21}.\left(46+.3\right)\right]\)
\(=7^{25}:\left(7^{21}.49\right)\)
\(=7^{25}:\left(7^{21}.7^2\right)\)
\(=7^{25}:7^{21+2}\)
\(=7^{25}:7^{23}\)
\(=7^{25-23}\)
\(=7^2\)
\(=49\)
46.(-123)-46.(-21)+46.2
46. [(-123)-(-21)+2]
=46.[(-102)+2]
=46.(-100)
=-4600
46 . (-123) - 46 . (-21) + 46 . 2
= 46 . [(-123) - (-21) + 2]
= 46 . (-100)
= -4600
a) \(...=-\dfrac{12}{46}-\dfrac{15}{21}+\dfrac{3}{7}-\dfrac{7}{23}\)
\(=-\dfrac{12}{46}-\dfrac{7}{23}-\dfrac{15}{21}+\dfrac{3}{7}\)
\(=-\dfrac{6}{23}-\dfrac{7}{23}-\dfrac{5}{7}+\dfrac{3}{7}\)
\(=-\dfrac{13}{23}-\dfrac{2}{7}\)
\(=-\dfrac{13.7}{23.7}-\dfrac{2.23}{23.7}\)
\(=-\dfrac{91}{161}-\dfrac{46}{161}=-\dfrac{137}{161}\)
b) \(...=-21+\dfrac{7}{9}-\dfrac{3}{17}+\dfrac{25}{9}\)
\(=-21-\dfrac{3}{17}+\dfrac{7}{9}+\dfrac{25}{9}\)
\(=-21-\dfrac{3}{17}+\dfrac{32}{9}\)
\(=-\dfrac{3213}{153}-\dfrac{27}{153}+\dfrac{544}{153}=-\dfrac{2696}{153}\)
21 x 54 + 21 x 46 + (-2000).
= 21 x (54 + 46) - 2000.
= 21 x 100 - 2000.
= 2100 - 2000.
= 100.