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[1/5 (9)^5-4(9)^3+5(-7)]-[( 1/5 (-7)^5-4(-7)^3+5(-7)]

Guest Apr 24, 2017
#1
+7629
0

[1/5 (9)^5-4(9)^3+5(-7)]-[( 1/5 (-7)^5-4(-7)^3+5(-7)]

$$[\frac{1}{5}\cdot 9^5-4\cdot 9^3+5\cdot (-7)]-[\frac{1}{5}\cdot (-7)^5-4\cdot (-7)^3+5\cdot (-7)]$$

$$=[11809.8-2916-35]-[-3361.4+1372-35]$$

$$=[8858.8]-[-2024.4]$$

$$=10883.2$$

!

asinus  Apr 24, 2017
edited by asinus  Apr 24, 2017
#2
+94118
+3

[1/5 (9)^5-4(9)^3+5(-7)]-[( 1/5 (-7)^5-4(-7)^3+5(-7)]

I am going to do it without a calculator!

$$[\frac{ (9)^5}{5}-4(9)^3+5(-7)]\quad -\quad [\frac{ (-7)^5}{5}-4(-7)^3+5(-7)]\\ =[\frac{ (9)^5}{5}-4(9)^3-35]\quad -\quad [\frac{ -(7)^5}{5}+4*7^3-35]\\ =\frac{ (9)^5}{5}-4(9)^3-35 \quad +\quad \frac{ +(7)^5}{5}-4*7^3+35\\ =\frac{ (9)^5}{5}-4(9)^3 \quad +\quad \frac{ +(7)^5}{5}-4*7^3\\ =\frac{9^3}{5}(9^2-20) \quad +\quad \frac{ 7^3}{5}(7^2-20)\\ =\frac{729}{5}(61) \quad +\quad \frac{ 343}{5}(29)\\ =\frac{729}{5}(60)+ \frac{729}{5}+\quad \frac{ 343}{5}(30)-\frac{ 343}{5}\\ =729*12+ \frac{730}{5}-\frac{1}{5}+\quad 343*6-\frac{ 345}{5}+\frac{2}{5}\\ =729*12+ \frac{385}{5}+\quad 343*6+\frac{1}{5}\\ =729*12+ \frac{385}{5}+\quad 343*6+\frac{1}{5}\\ =729*12+77+\quad 343*6+\frac{1}{5}\\ =6*1458+77+\quad 343*6+\frac{1}{5}\\ =6*1801+77+\quad \frac{1}{5}\\ =10806+77+\quad \frac{1}{5}\\ =10883\frac{1}{5}\\$$

Melody  Apr 24, 2017