How do you evaluate $(10 x^{6} - 12 x^{5} + 18 x^{4} - 20 x^{3}) \div (2 x^{7})$ $(10x ^ { 6} - 12x ^ { 5} + 18x ^ { 4} - 20x ^ { 3} ) \div ( 2x ^ { 7} )$ ?

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Answer 1 · 2017-01-02T12:08:11

$5 x^{- 1} - 6 x^{- 2} + 9 x^{- 3} - 10 x^{- 4}$ $5x^-1-6x^-2+9x^-3-10x^-4$

$(10 x^{6} - 12 x^{5} + 18 x^{4} - 20 x^{3}) \div (2 x^{7})$ $(10x^6-12x^5+18x^4-20x^3)-:(2x^7)$

by long division:

$\frac{10 x^{6} - 12^{5} + 18 x^{4} - 20 x^{3}}{2 x^{7}}$ $(10x^6-12^5+18x^4-20x^3)/(2x^7)$

$= 5 x^{- 1} - 6 x^{- 2} + 9 x^{- 3} - 10 x^{- 4}$ $=5x^-1-6x^-2+9x^-3-10x^-4$

check:

$2 x^{7} (5 x^{- 1} - 6 x^{- 2} + 9 x^{- 3} - 10 x^{- 4})$ $2x^7(5x^-1-6x^-2+9x^-3-10x^-4)$

$= (10 x^{- 1 + 7} - 12 x^{- 2 + 7} + 18 x^{- 3 + 7} - 20 x^{- 4 + 7})$ $=(10x^(-1+7)-12x^(-2+7)+18x^(-3+7)-20x^(-4+7))$

$= (10 x^{6} - 12 x^{5} + 18 x^{4} - 20 x^{3})$ $=(10x^6-12x^5+18x^4-20x^3)$

Take note: $a^{3} \cdot a^{4} = a^{3 + 4}$ $a^3*a^4=a^(3+4)$ and $\frac{a^{m}}{a^{n}} = a^{m - n}$ $a^m/a^n=a^(m-n)$ $m > n$ $m>n$

How do you evaluate (10x6−12x5+18x4−20x3)÷(2x7)(10x ^ { 6} - 12x ^ { 5} + 18x ^ { 4} - 20x ^ { 3} ) \div ( 2x ^ { 7} )?